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leirui pushed a commit to branch research/area-visualization
in repository https://gitbox.apache.org/repos/asf/iotdb.git

commit d545f8db5f54b4a53d7018e446127d1ed1e889c4
Author: Lei Rui <[email protected]>
AuthorDate: Thu Jan 23 22:35:46 2025 +0800

    eBUG_build
---
 server/pom.xml                                     |  23 +
 .../java/org/apache/iotdb/db/query/eBUG/Point.java |  48 +-
 .../org/apache/iotdb/db/query/eBUG/Polyline.java   |  53 +-
 .../java/org/apache/iotdb/db/query/eBUG/Test1.java | 126 ++--
 .../java/org/apache/iotdb/db/query/eBUG/Test2.java |  86 +--
 .../java/org/apache/iotdb/db/query/eBUG/Test3.java |  91 +++
 .../java/org/apache/iotdb/db/query/eBUG/Tmp.java   |  58 +-
 .../java/org/apache/iotdb/db/query/eBUG/Tool.java  | 365 +++++------
 .../org/apache/iotdb/db/query/eBUG/Triangle.java   |  76 +--
 .../java/org/apache/iotdb/db/query/eBUG/eBUG.java  | 681 +++++++++++----------
 .../org/apache/iotdb/db/query/eBUG/eBUG_Build.java | 139 +++++
 11 files changed, 1035 insertions(+), 711 deletions(-)

diff --git a/server/pom.xml b/server/pom.xml
index 3ca3b695285..51f9a56c69a 100644
--- a/server/pom.xml
+++ b/server/pom.xml
@@ -278,6 +278,29 @@
                     </execution>
                 </executions>
             </plugin>
+            <plugin>
+                <artifactId>maven-assembly-plugin</artifactId>
+                <configuration>
+                    <finalName>eBUG_Build</finalName>
+                    <archive>
+                        <manifest>
+                            
<mainClass>org.apache.iotdb.db.query.eBUG.eBUG_Build</mainClass>
+                        </manifest>
+                    </archive>
+                    <descriptorRefs>
+                        <descriptorRef>jar-with-dependencies</descriptorRef>
+                    </descriptorRefs>
+                </configuration>
+                <executions>
+                    <execution>
+                        <id>make-assembly</id>
+                        <phase>package</phase>
+                        <goals>
+                            <goal>single</goal>
+                        </goals>
+                    </execution>
+                </executions>
+            </plugin>
         </plugins>
     </build>
     <profiles>
diff --git a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Point.java 
b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Point.java
index 6e6fc3aa91e..e9bcf241f0f 100644
--- a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Point.java
+++ b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Point.java
@@ -2,33 +2,33 @@ package org.apache.iotdb.db.query.eBUG;
 
 public class Point {
 
-    double x, y, z;
+  double x, y, z;
 
-    public Point prev; // 指向T'_max{0,k-e}里当前点的前一个点 for eBUG usage
-    public Point next; // 指向T'_max{0,k-e}里当前点的后一个点 for eBUG usage
-    // 注意Triangle里的prev&next用于最新状态下存在三角形之间的连接关系,
-    // 而这里Point的prev&next用于滞后e个淘汰点(也就是最近的e个淘汰点先不施加)状态下的未淘汰点之间的连接关系
+  public Point prev; // 指向T'_max{0,k-e}里当前点的前一个点 for eBUG usage
+  public Point next; // 指向T'_max{0,k-e}里当前点的后一个点 for eBUG usage
+  // 注意Triangle里的prev&next用于最新状态下存在三角形之间的连接关系,
+  // 而这里Point的prev&next用于滞后e个淘汰点(也就是最近的e个淘汰点先不施加)状态下的未淘汰点之间的连接关系
 
-    public Point(double x, double y) {
-        this.x = x;
-        this.y = y;
-        this.z = Double.POSITIVE_INFINITY; // effective area
+  public Point(double x, double y) {
+    this.x = x;
+    this.y = y;
+    this.z = Double.POSITIVE_INFINITY; // effective area
 
-        // for eBUG usage
-//        this.eliminated = false;
-        this.prev = null;
-        this.next = null;
-    }
+    // for eBUG usage
+    //        this.eliminated = false;
+    this.prev = null;
+    this.next = null;
+  }
 
-    public void markEliminated() {
-        // to avoid traversing each point between pa to pb,
-        // instead only traversing at most e most recently eliminated points 
lagged
-        prev.next = next;
-        next.prev = prev;
-    }
+  public void markEliminated() {
+    // to avoid traversing each point between pa to pb,
+    // instead only traversing at most e most recently eliminated points lagged
+    prev.next = next;
+    next.prev = prev;
+  }
 
-    @Override
-    public String toString() {
-        return "Point: (" + x + ", " + y + ", " + z + ")";
-    }
+  @Override
+  public String toString() {
+    return "Point: (" + x + ", " + y + ", " + z + ")";
+  }
 }
diff --git a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Polyline.java 
b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Polyline.java
index 1ddfe2ebbe1..534c7a6f67e 100644
--- a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Polyline.java
+++ b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Polyline.java
@@ -5,31 +5,30 @@ import java.util.List;
 
 public class Polyline {
 
-    private List<Point> vertices = new ArrayList<>();
-
-    public void addVertex(Point point) {
-//        if (!vertices.isEmpty()) { //before adding this point
-//            vertices.get(vertices.size() - 1).next = point;
-//            point.prev = vertices.get(vertices.size() - 1);
-//        }
-        vertices.add(point);
-    }
-
-    public List<Point> getVertices() {
-//        return new ArrayList<>(vertices);
-        return vertices;
-    }
-
-
-    public int size() {
-        return vertices.size();
-    }
-
-    public Point get(int index) {
-        return vertices.get(index);
-    }
-
-    public void clear() {
-        vertices.clear();
-    }
+  private List<Point> vertices = new ArrayList<>();
+
+  public void addVertex(Point point) {
+    //        if (!vertices.isEmpty()) { //before adding this point
+    //            vertices.get(vertices.size() - 1).next = point;
+    //            point.prev = vertices.get(vertices.size() - 1);
+    //        }
+    vertices.add(point);
+  }
+
+  public List<Point> getVertices() {
+    //        return new ArrayList<>(vertices);
+    return vertices;
+  }
+
+  public int size() {
+    return vertices.size();
+  }
+
+  public Point get(int index) {
+    return vertices.get(index);
+  }
+
+  public void clear() {
+    vertices.clear();
+  }
 }
diff --git a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Test1.java 
b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Test1.java
index 91df7751e50..385362b9e6b 100644
--- a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Test1.java
+++ b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Test1.java
@@ -10,74 +10,82 @@ import java.util.Random;
 import static org.apache.iotdb.db.query.eBUG.eBUG.buildEffectiveArea;
 
 public class Test1 {
-    // 用于验证Java eBUG实现和python版本(e=0/1)结果的一致性
-    public static void main(String[] args) {
-        Polyline polyline = new Polyline();
-        List<Polyline> polylineList = new ArrayList<>();
-        Random rand = new Random(10);
-        int n = 10000;
-        int eParam = 0;
+  // 用于验证Java eBUG实现和python版本(e=0/1)结果的一致性
+  public static void main(String[] args) {
+    Polyline polyline = new Polyline();
+    List<Polyline> polylineList = new ArrayList<>();
+    Random rand = new Random(10);
+    int n = 10000;
+    int eParam = 1;
 
-        int p = 10;
-        for (int i = 0; i < n; i += p) {
-            Polyline polylineBatch = new Polyline();
-            for (int j = i; j < Math.min(i + p, n); j++) {
-                double v = rand.nextInt(1000000);
+    int p = 10;
+    for (int i = 0; i < n; i += p) {
+      Polyline polylineBatch = new Polyline();
+      for (int j = i; j < Math.min(i + p, n); j++) {
+        double v = rand.nextInt(1000000);
 
-                polyline.addVertex(new Point(j, v));
+        polyline.addVertex(new Point(j, v));
 
-                polylineBatch.addVertex(new Point(j, v));
-            }
-            polylineList.add(polylineBatch);
-        }
+        polylineBatch.addVertex(new Point(j, v));
+      }
+      polylineList.add(polylineBatch);
+    }
 
-        try (FileWriter writer = new FileWriter("raw.csv")) {
-            // 写入CSV头部
-            writer.append("x,y,z\n");
+    try (FileWriter writer = new FileWriter("raw.csv")) {
+      // 写入CSV头部
+      writer.append("x,y,z\n");
 
-            // 写入每个点的数据
-            for (int i = 0; i < polyline.size(); i++) {
-                Point point = polyline.get(i);
-                writer.append(point.x + "," + point.y + "," + point.z + "\n");
-            }
-            System.out.println("Data has been written");
-        } catch (IOException e) {
-            System.out.println("Error writing to CSV file: " + e.getMessage());
-        }
+      // 写入每个点的数据
+      for (int i = 0; i < polyline.size(); i++) {
+        Point point = polyline.get(i);
+        writer.append(point.x + "," + point.y + "," + point.z + "\n");
+      }
+      System.out.println("Data has been written");
+    } catch (IOException e) {
+      System.out.println("Error writing to CSV file: " + e.getMessage());
+    }
 
-        System.out.println("---------------------------------");
-        long startTime = System.currentTimeMillis();
-        // 注意现在返回的结果是按照Sig递增也就是bottom-up淘汰的顺序排列的,而不是按照时间戳递增排列
-        List<Point> results = buildEffectiveArea(polyline, eParam, false);
-        // 输出结果
-        long endTime = System.currentTimeMillis();
-        System.out.println("n=" + n + ", e=" + eParam + ", Time taken to 
reduce points: " + (endTime - startTime) + "ms");
-        System.out.println(results.size());
+    System.out.println("---------------------------------");
+    long startTime = System.currentTimeMillis();
+    // 注意现在返回的结果是按照Sig递增也就是bottom-up淘汰的顺序排列的,而不是按照时间戳递增排列
+    List<Point> results = buildEffectiveArea(polyline, eParam, false);
+    // 输出结果
+    long endTime = System.currentTimeMillis();
+    System.out.println(
+        "n="
+            + n
+            + ", e="
+            + eParam
+            + ", Time taken to reduce points: "
+            + (endTime - startTime)
+            + "ms");
+    System.out.println(results.size());
 
-        // 注意现在返回的结果是按照Sig递增也就是bottom-up淘汰的顺序排列的,而不是按照时间戳递增排列
-        // 按照时间戳递增排序整理:
-        results.sort(Comparator.comparingDouble(point -> point.x));
+    // 注意现在返回的结果是按照Sig递增也就是bottom-up淘汰的顺序排列的,而不是按照时间戳递增排列
+    // 按照时间戳递增排序整理:
+    System.out.println("make the bottom-up results sorted by time:");
+    results.sort(Comparator.comparingDouble(point -> point.x));
 
-        if (results.size() <= 100) {
-            System.out.println("+++++++++++++++++++");
-            for (int i = 0; i < results.size(); i++) {
-                Point point = results.get(i);
-                System.out.println("Point: (" + point.x + ", " + point.y + ", 
" + point.z + ")");
-            }
-        }
+    if (results.size() <= 100) {
+      System.out.println("+++++++++++++++++++");
+      for (int i = 0; i < results.size(); i++) {
+        Point point = results.get(i);
+        System.out.println("Point: (" + point.x + ", " + point.y + ", " + 
point.z + ")");
+      }
+    }
 
-        try (FileWriter writer = new FileWriter("fast.csv")) {
-            // 写入CSV头部
-            writer.append("x,y,z\n");
+    try (FileWriter writer = new FileWriter("fast.csv")) {
+      // 写入CSV头部
+      writer.append("x,y,z\n");
 
-            // 写入每个点的数据
-            for (int i = 0; i < results.size(); i++) {
-                Point point = results.get(i);
-                writer.append(point.x + "," + point.y + "," + point.z + "\n");
-            }
-            System.out.println("Data has been written");
-        } catch (IOException e) {
-            System.out.println("Error writing to CSV file: " + e.getMessage());
-        }
+      // 写入每个点的数据
+      for (int i = 0; i < results.size(); i++) {
+        Point point = results.get(i);
+        writer.append(point.x + "," + point.y + "," + point.z + "\n");
+      }
+      System.out.println("Data has been written");
+    } catch (IOException e) {
+      System.out.println("Error writing to CSV file: " + e.getMessage());
     }
+  }
 }
diff --git a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Test2.java 
b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Test2.java
index fb7de582f17..6cb0accefaa 100644
--- a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Test2.java
+++ b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Test2.java
@@ -9,44 +9,52 @@ import java.util.Random;
 import static org.apache.iotdb.db.query.eBUG.eBUG.buildEffectiveArea;
 
 public class Test2 {
-    // 用于测试在线采样
-    public static void main(String[] args) {
-        int n = 20;
-        int eParam = 1;
-
-        int m = 2; // >2代表在线采样,<=2代表预计算
-//        for (int m = 9900; m <= n; m++) {
-
-        Polyline polyline = new Polyline();
-        Random rand = new Random(2);
-        for (int i = 0; i < n; i++) {
-            double v = rand.nextInt(1000000);
-            polyline.addVertex(new Point(i, v));
-        }
-
-        long startTime = System.currentTimeMillis();
-        List<Point> results = buildEffectiveArea(polyline, eParam, false, m);
-        long endTime = System.currentTimeMillis();
-        System.out.println("n=" + n + ", e=" + eParam + ", Time taken to 
reduce points: " + (endTime - startTime) + "ms");
-
-        System.out.println(results.size());
-        if (m > 2 && m < n) {
-            Assert.isTrue(results.size() == m);
-        } else {
-            Assert.isTrue(results.size() == n);
-        }
-        if (results.size() <= 100) {
-            System.out.println("+++++++++++++++++++");
-            for (Point point : results) {
-                System.out.println("Point: (" + point.x + ", " + point.y + ", 
" + point.z + ")");
-            }
-            // 注意现在返回的结果是按照Sig递增也就是bottom-up淘汰的顺序排列的,而不是按照时间戳递增排列
-            // 按照时间戳递增排序整理:
-            results.sort(Comparator.comparingDouble(point -> point.x));
-            System.out.println("+++++++++++++++++++");
-            for (Point point : results) {
-                System.out.println("Point: (" + point.x + ", " + point.y + ", 
" + point.z + ")");
-            }
-        }
+  // 用于测试在线采样
+  public static void main(String[] args) {
+    int n = 20;
+    int eParam = 1;
+
+    int m = 2; // >2代表在线采样,<=2代表预计算
+    //        for (int m = 9900; m <= n; m++) {
+
+    Polyline polyline = new Polyline();
+    Random rand = new Random(2);
+    for (int i = 0; i < n; i++) {
+      double v = rand.nextInt(1000000);
+      polyline.addVertex(new Point(i, v));
     }
+
+    long startTime = System.currentTimeMillis();
+    List<Point> results = buildEffectiveArea(polyline, eParam, false, m);
+    long endTime = System.currentTimeMillis();
+    System.out.println(
+        "n="
+            + n
+            + ", e="
+            + eParam
+            + ", Time taken to reduce points: "
+            + (endTime - startTime)
+            + "ms");
+
+    System.out.println(results.size());
+    if (m > 2 && m < n) {
+      Assert.isTrue(results.size() == m);
+    } else {
+      Assert.isTrue(results.size() == n);
+    }
+    if (results.size() <= 100) {
+      System.out.println("+++++++++++++++++++");
+      for (Point point : results) {
+        System.out.println("Point: (" + point.x + ", " + point.y + ", " + 
point.z + ")");
+      }
+      // 注意现在返回的结果是按照Sig递增也就是bottom-up淘汰的顺序排列的,而不是按照时间戳递增排列
+      // 按照时间戳递增排序整理:
+      System.out.println("make the bottom-up results sorted by time:");
+      results.sort(Comparator.comparingDouble(point -> point.x));
+      System.out.println("+++++++++++++++++++");
+      for (Point point : results) {
+        System.out.println("Point: (" + point.x + ", " + point.y + ", " + 
point.z + ")");
+      }
+    }
+  }
 }
diff --git a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Test3.java 
b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Test3.java
new file mode 100644
index 00000000000..d17ea8fcc65
--- /dev/null
+++ b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Test3.java
@@ -0,0 +1,91 @@
+package org.apache.iotdb.db.query.eBUG;
+
+import java.io.FileWriter;
+import java.io.IOException;
+import java.util.ArrayList;
+import java.util.Comparator;
+import java.util.List;
+import java.util.Random;
+
+import static org.apache.iotdb.db.query.eBUG.eBUG.buildEffectiveArea;
+
+public class Test3 {
+  // 用于验证Java eBUG实现和python版本(e=0/1)结果的一致性
+  public static void main(String[] args) {
+    Polyline polyline = new Polyline();
+    List<Polyline> polylineList = new ArrayList<>();
+    Random rand = new Random(10);
+    int n = 10000;
+    int eParam = 0;
+
+    int p = 10;
+    for (int i = 0; i < n; i += p) {
+      Polyline polylineBatch = new Polyline();
+      for (int j = i; j < Math.min(i + p, n); j++) {
+        double v = rand.nextInt(1000000);
+
+        polyline.addVertex(new Point(j, v));
+
+        polylineBatch.addVertex(new Point(j, v));
+      }
+      polylineList.add(polylineBatch);
+    }
+
+    try (FileWriter writer = new FileWriter("raw.csv")) {
+      // 写入CSV头部
+      writer.append("x,y,z\n");
+
+      // 写入每个点的数据
+      for (int i = 0; i < polyline.size(); i++) {
+        Point point = polyline.get(i);
+        writer.append(point.x + "," + point.y + "," + point.z + "\n");
+      }
+      System.out.println("Data has been written");
+    } catch (IOException e) {
+      System.out.println("Error writing to CSV file: " + e.getMessage());
+    }
+
+    System.out.println("---------------------------------");
+    long startTime = System.currentTimeMillis();
+    // 注意现在返回的结果是按照Sig递增也就是bottom-up淘汰的顺序排列的,而不是按照时间戳递增排列
+    List<Point> results = buildEffectiveArea(polyline, eParam, false);
+    // 输出结果
+    long endTime = System.currentTimeMillis();
+    System.out.println(
+        "n="
+            + n
+            + ", e="
+            + eParam
+            + ", Time taken to reduce points: "
+            + (endTime - startTime)
+            + "ms");
+    System.out.println(results.size());
+
+    // 注意现在返回的结果是按照Sig递增也就是bottom-up淘汰的顺序排列的,而不是按照时间戳递增排列
+    // 按照时间戳递增排序整理:
+    System.out.println("make the bottom-up results sorted by time:");
+    results.sort(Comparator.comparingDouble(point -> point.x));
+
+    if (results.size() <= 100) {
+      System.out.println("+++++++++++++++++++");
+      for (int i = 0; i < results.size(); i++) {
+        Point point = results.get(i);
+        System.out.println("Point: (" + point.x + ", " + point.y + ", " + 
point.z + ")");
+      }
+    }
+
+    try (FileWriter writer = new FileWriter("fast.csv")) {
+      // 写入CSV头部
+      writer.append("x,y,z\n");
+
+      // 写入每个点的数据
+      for (int i = 0; i < results.size(); i++) {
+        Point point = results.get(i);
+        writer.append(point.x + "," + point.y + "," + point.z + "\n");
+      }
+      System.out.println("Data has been written");
+    } catch (IOException e) {
+      System.out.println("Error writing to CSV file: " + e.getMessage());
+    }
+  }
+}
diff --git a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Tmp.java 
b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Tmp.java
index 9cfb8ac3d5f..270aca1dee7 100644
--- a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Tmp.java
+++ b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Tmp.java
@@ -8,35 +8,37 @@ import java.util.PriorityQueue;
 import java.util.Random;
 
 public class Tmp {
-    // 用于debug为什么n>2kw的耗时增大明显
-    public static void main(String[] args) {
-        int seed = 10;
-        Random rand = new Random(seed);
-        int eParam = 1;
-        try (PrintWriter writer = new PrintWriter(new File("tmp.csv"))) {
-            for (int n = 100_0000; n < 100000_0000; n += 5000_0000) { // 
超过两千万就都变得慢多了,感觉可能是内存有限的原因,而不是算法复杂度
-//            for (int n = 19000000; n < 3000_0000; n +=200_0000) {
-                PriorityQueue<Point> heap = new 
PriorityQueue<>(Comparator.comparingDouble(t -> t.y));
-                for (int i = 0; i < n; i++) {
-                    double v = rand.nextInt(1000000);
-                    heap.add(new Point(i, v));
-                }
-
-                long startTime = System.currentTimeMillis();
-                long sum = 0;
-                while (!heap.isEmpty()) {
-                    Point p = heap.poll();
-                    sum += p.x;
-                }
-                long endTime = System.currentTimeMillis();
-                System.out.println(n + ", Time taken to reduce points: " + 
(endTime - startTime) + "ms");
-                writer.println(n + "," + "0" + "," + (endTime - startTime));
-                System.out.println(sum);
-            }
-        } catch (FileNotFoundException e) {
-            throw new RuntimeException(e);
+  // 用于debug为什么n>2kw的耗时增大明显
+  public static void main(String[] args) {
+    int seed = 10;
+    Random rand = new Random(seed);
+    int eParam = 1;
+    try (PrintWriter writer = new PrintWriter(new File("tmp.csv"))) {
+      for (int n = 100_0000;
+          n < 100000_0000;
+          n += 5000_0000) { // 超过两千万就都变得慢多了,感觉可能是内存有限的原因,而不是算法复杂度
+        //            for (int n = 19000000; n < 3000_0000; n +=200_0000) {
+        PriorityQueue<Point> heap = new 
PriorityQueue<>(Comparator.comparingDouble(t -> t.y));
+        for (int i = 0; i < n; i++) {
+          double v = rand.nextInt(1000000);
+          heap.add(new Point(i, v));
         }
 
-        System.out.println("finish");
+        long startTime = System.currentTimeMillis();
+        long sum = 0;
+        while (!heap.isEmpty()) {
+          Point p = heap.poll();
+          sum += p.x;
+        }
+        long endTime = System.currentTimeMillis();
+        System.out.println(n + ", Time taken to reduce points: " + (endTime - 
startTime) + "ms");
+        writer.println(n + "," + "0" + "," + (endTime - startTime));
+        System.out.println(sum);
+      }
+    } catch (FileNotFoundException e) {
+      throw new RuntimeException(e);
     }
+
+    System.out.println("finish");
+  }
 }
diff --git a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Tool.java 
b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Tool.java
index f7c5bbfb668..86658e24385 100644
--- a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Tool.java
+++ b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Tool.java
@@ -1,199 +1,204 @@
 package org.apache.iotdb.db.query.eBUG;
 
-
 import java.util.ArrayList;
 import java.util.Collections;
 import java.util.List;
 
 public class Tool {
-    // 计算三角形面积
-    public static double triArea(Point d0, Point d1, Point d2) {
-        double dArea = ((d1.x - d0.x) * (d2.y - d0.y) - (d2.x - d0.x) * (d1.y 
- d0.y)) / 2.0;
-        return (dArea > 0.0) ? dArea : -dArea; // abs
+  // 计算三角形面积
+  public static double triArea(Point d0, Point d1, Point d2) {
+    double dArea = ((d1.x - d0.x) * (d2.y - d0.y) - (d2.x - d0.x) * (d1.y - 
d0.y)) / 2.0;
+    return (dArea > 0.0) ? dArea : -dArea; // abs
+  }
+
+  // 计算简单多边形(边不交叉)的面积(鞋带公式)
+  public static double calculatePolygonArea(List<Point> points) {
+    // points多边形顶点,要求按照逆时针或者顺时针的顺序枚举,否则鞋带公式无法给出正确结果
+    int n = points.size();
+    double area = 0;
+    for (int i = 0; i < n; i++) {
+      int next = (i + 1) % n;
+      area += points.get(i).x * points.get(next).y - points.get(next).x * 
points.get(i).y;
     }
-
-    // 计算简单多边形(边不交叉)的面积(鞋带公式)
-    public static double calculatePolygonArea(List<Point> points) {
-        // points多边形顶点,要求按照逆时针或者顺时针的顺序枚举,否则鞋带公式无法给出正确结果
-        int n = points.size();
-        double area = 0;
-        for (int i = 0; i < n; i++) {
-            int next = (i + 1) % n;
-            area += points.get(i).x * points.get(next).y - points.get(next).x 
* points.get(i).y;
-        }
-        return Math.abs(area) / 2.0;
+    return Math.abs(area) / 2.0;
+  }
+
+  // 计算两个向量的叉积
+  public static double crossProduct(double x1, double y1, double x2, double 
y2) {
+    //  >0: (x2,y2)在(x1,y1)的逆时针方向
+    //  <0: (x2,y2)在(x1,y1)的顺时针方向
+    //  =0: 平行或共线
+    return x1 * y2 - y1 * x2;
+  }
+
+  // 判断两条线段是否相交并计算交点
+  // L1包含一个线段的两个端点,L2包含另一个线段的两个端点
+  public static Object[] lineIntersection(Point[] L1, Point[] L2) {
+    double x1 = L1[0].x, y1 = L1[0].y, x2 = L1[1].x, y2 = L1[1].y;
+    double x3 = L2[0].x, y3 = L2[0].y, x4 = L2[1].x, y4 = L2[1].y;
+
+    // 判断是否相交(叉积)
+    double d1 = crossProduct(x2 - x1, y2 - y1, x3 - x1, y3 - y1);
+    double d2 = crossProduct(x2 - x1, y2 - y1, x4 - x1, y4 - y1);
+    double d3 = crossProduct(x4 - x3, y4 - y3, x1 - x3, y1 - y3);
+    double d4 = crossProduct(x4 - x3, y4 - y3, x2 - x3, y2 - y3);
+
+    // 如果叉积条件满足,表示有交点
+    // d1*d2<0意味着P3、P4分别在L12的两边
+    // d3*d4<0意味着P1、P2分别在L34的两边
+    // 两个同时满足说明有交点
+    if (d1 * d2 < 0 && d3 * d4 < 0) {
+      double denominator = (y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1); // 
不可能为0(平行或共线),因为已经判断相交了
+      double t1 = ((x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3)) / 
denominator;
+      double x = x1 + t1 * (x2 - x1);
+      double y = y1 + t1 * (y2 - y1);
+      return new Object[] {true, new Point(x, y)};
     }
 
-    // 计算两个向量的叉积
-    public static double crossProduct(double x1, double y1, double x2, double 
y2) {
-        //  >0: (x2,y2)在(x1,y1)的逆时针方向
-        //  <0: (x2,y2)在(x1,y1)的顺时针方向
-        //  =0: 平行或共线
-        return x1 * y2 - y1 * x2;
+    // 检查是否起点或终点重合
+    if ((x1 == x3 && y1 == y3) || (x1 == x4 && y1 == y4)) {
+      return new Object[] {true, new Point(x1, y1)};
     }
-
-    // 判断两条线段是否相交并计算交点
-    // L1包含一个线段的两个端点,L2包含另一个线段的两个端点
-    public static Object[] lineIntersection(Point[] L1, Point[] L2) {
-        double x1 = L1[0].x, y1 = L1[0].y, x2 = L1[1].x, y2 = L1[1].y;
-        double x3 = L2[0].x, y3 = L2[0].y, x4 = L2[1].x, y4 = L2[1].y;
-
-        // 判断是否相交(叉积)
-        double d1 = crossProduct(x2 - x1, y2 - y1, x3 - x1, y3 - y1);
-        double d2 = crossProduct(x2 - x1, y2 - y1, x4 - x1, y4 - y1);
-        double d3 = crossProduct(x4 - x3, y4 - y3, x1 - x3, y1 - y3);
-        double d4 = crossProduct(x4 - x3, y4 - y3, x2 - x3, y2 - y3);
-
-        // 如果叉积条件满足,表示有交点
-        // d1*d2<0意味着P3、P4分别在L12的两边
-        // d3*d4<0意味着P1、P2分别在L34的两边
-        // 两个同时满足说明有交点
-        if (d1 * d2 < 0 && d3 * d4 < 0) {
-            double denominator = (y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - 
y1); // 不可能为0(平行或共线),因为已经判断相交了
-            double t1 = ((x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3)) / 
denominator;
-            double x = x1 + t1 * (x2 - x1);
-            double y = y1 + t1 * (y2 - y1);
-            return new Object[]{true, new Point(x, y)};
-        }
-
-        // 检查是否起点或终点重合
-        if ((x1 == x3 && y1 == y3) || (x1 == x4 && y1 == y4)) {
-            return new Object[]{true, new Point(x1, y1)};
-        }
-        if ((x2 == x3 && y2 == y3) || (x2 == x4 && y2 == y4)) {
-            return new Object[]{true, new Point(x2, y2)};
-        }
-
-        return new Object[]{false, null};
+    if ((x2 == x3 && y2 == y3) || (x2 == x4 && y2 == y4)) {
+      return new Object[] {true, new Point(x2, y2)};
     }
 
-    // 计算总的多边形面积(通过时间序列扫描交点),默认要求点按照时间戳严格递增排列
-    public static double total_areal_displacement(List<Point> points, 
List<Point> points2, boolean debug) {
-        double totalArea = 0;
-        int i = 0, j = 0; // i for points, j for points2
-        Point prevIntersection = null;
-        int prevI = -1, prevJ = -1;
-
-//        List<double[]> intersectionCoords = new ArrayList<>();
-        List<Double> areaList = new ArrayList<>();
-
-        while (i < points.size() - 1 && j < points2.size() - 1) {
-            if (debug) {
-                System.out.println("--------- " + i + " " + j + " 
------------");
-            }
-
-            // 当前线段
-            Point[] L1 = {points.get(i), points.get(i + 1)};
-            Point[] L2 = {points2.get(j), points2.get(j + 1)};
-
-            // 判断是否有交点
-            Object[] result = lineIntersection(L1, L2);
-            boolean isIntersect = (boolean) result[0];
-            Point intersection = (Point) result[1];
-
-            if (isIntersect) {
-//                intersectionCoords.add(intersection);
-
-                if (prevIntersection != null) {
-                    // 构造多边形点集
-                    List<Point> polygon = new ArrayList<>(); // 
按照顺时针/逆时针几何连接顺序枚举多边形的顶点
-                    polygon.add(prevIntersection);
-                    if (debug) {
-                        System.out.println("- start intersection: " + 
prevIntersection);
-                    }
-                    polygon.addAll(points.subList(prevI, i + 1)); // 
添加当前线段的点,左闭右开
-//                    polygon.addAll(Arrays.asList(Arrays.copyOfRange(points, 
prevI, i + 1)));  // 添加当前线段的点,左闭右开
-                    if (debug) {
-                        System.out.println("- one side: " + 
points.subList(prevI, i + 1));
-                    }
-                    polygon.add(intersection);
-                    if (debug) {
-                        System.out.println("- end intersection: " + 
intersection);
-                    }
-                    List<Point> tempPoints2 = points2.subList(prevJ, j + 1);
-                    Collections.reverse(tempPoints2);  // 添加另一序列的点
-                    polygon.addAll(tempPoints2);
-                    if (debug) {
-                        System.out.println("- another side: " + tempPoints2);
-                    }
-
-//                    double[][] polygonArray = new double[polygon.size()][2];
-//                    for (int k = 0; k < polygon.size(); k++) {
-//                        polygonArray[k] = polygon.get(k);
-//                    }
-
-                    // 计算多边形面积,注意polygon里的点一定是按照顺时针/逆时针几何连接顺序枚举的多边形顶点
-                    double area = calculatePolygonArea(polygon);
-                    if (debug) {
-                        System.out.println("Area = " + area);
-                    }
-                    totalArea += area;
-                    areaList.add(area);
-                }
-
-                prevIntersection = intersection;
-                prevI = i + 1;
-                prevJ = j + 1;
-                if (debug) {
-                    System.out.println("This intersection = " + intersection
-                            + ", next polygon: side1 = " + prevI + ", side2 = 
" + prevJ);
-                }
-            }
-
-
-            int currentI = i; // 临时存储i
-            int currentJ = j; // 临时存储j
-            if (points.get(currentI + 1).x <= points2.get(currentJ + 1).x) {
-                i += 1; // 基于时间戳严格递增的假设,Line不会回头或者垂直
-            }
-            if (points.get(currentI + 1).x >= points2.get(currentJ + 1).x) {
-                j += 1; // 基于时间戳严格递增的假设,Line不会回头或者垂直
-            }
-        } // end of while
+    return new Object[] {false, null};
+  }
+
+  // 计算总的多边形面积(通过时间序列扫描交点),默认要求点按照时间戳严格递增排列
+  public static double total_areal_displacement(
+      List<Point> points, List<Point> points2, boolean debug) {
+    double totalArea = 0;
+    int i = 0, j = 0; // i for points, j for points2
+    Point prevIntersection = null;
+    int prevI = -1, prevJ = -1;
+
+    //        List<double[]> intersectionCoords = new ArrayList<>();
+    List<Double> areaList = new ArrayList<>();
+
+    while (i < points.size() - 1 && j < points2.size() - 1) {
+      if (debug) {
+        System.out.println("--------- " + i + " " + j + " ------------");
+      }
+
+      // 当前线段
+      Point[] L1 = {points.get(i), points.get(i + 1)};
+      Point[] L2 = {points2.get(j), points2.get(j + 1)};
+
+      // 判断是否有交点
+      Object[] result = lineIntersection(L1, L2);
+      boolean isIntersect = (boolean) result[0];
+      Point intersection = (Point) result[1];
+
+      if (isIntersect) {
+        //                intersectionCoords.add(intersection);
+
+        if (prevIntersection != null) {
+          // 构造多边形点集
+          List<Point> polygon = new ArrayList<>(); // 按照顺时针/逆时针几何连接顺序枚举多边形的顶点
+          polygon.add(prevIntersection);
+          if (debug) {
+            System.out.println("- start intersection: " + prevIntersection);
+          }
+          polygon.addAll(points.subList(prevI, i + 1)); // 添加当前线段的点,左闭右开
+          //                    
polygon.addAll(Arrays.asList(Arrays.copyOfRange(points, prevI, i +
+          // 1)));  // 添加当前线段的点,左闭右开
+          if (debug) {
+            System.out.println("- one side: " + points.subList(prevI, i + 1));
+          }
+          polygon.add(intersection);
+          if (debug) {
+            System.out.println("- end intersection: " + intersection);
+          }
+          List<Point> tempPoints2 = points2.subList(prevJ, j + 1);
+          Collections.reverse(tempPoints2); // 添加另一序列的点
+          polygon.addAll(tempPoints2);
+          if (debug) {
+            System.out.println("- another side: " + tempPoints2);
+          }
+
+          //                    double[][] polygonArray = new 
double[polygon.size()][2];
+          //                    for (int k = 0; k < polygon.size(); k++) {
+          //                        polygonArray[k] = polygon.get(k);
+          //                    }
+
+          // 计算多边形面积,注意polygon里的点一定是按照顺时针/逆时针几何连接顺序枚举的多边形顶点
+          double area = calculatePolygonArea(polygon);
+          if (debug) {
+            System.out.println("Area = " + area);
+          }
+          totalArea += area;
+          areaList.add(area);
+        }
 
+        prevIntersection = intersection;
+        prevI = i + 1;
+        prevJ = j + 1;
         if (debug) {
-            System.out.println(areaList);
+          System.out.println(
+              "This intersection = "
+                  + intersection
+                  + ", next polygon: side1 = "
+                  + prevI
+                  + ", side2 = "
+                  + prevJ);
         }
-
-        return totalArea;
+      }
+
+      int currentI = i; // 临时存储i
+      int currentJ = j; // 临时存储j
+      if (points.get(currentI + 1).x <= points2.get(currentJ + 1).x) {
+        i += 1; // 基于时间戳严格递增的假设,Line不会回头或者垂直
+      }
+      if (points.get(currentI + 1).x >= points2.get(currentJ + 1).x) {
+        j += 1; // 基于时间戳严格递增的假设,Line不会回头或者垂直
+      }
+    } // end of while
+
+    if (debug) {
+      System.out.println(areaList);
     }
 
-    // 测试方法
-    public static void main(String[] args) {
-        // 示例数据
-        List<Point> points = new ArrayList<>();
-        points.add(new Point(0, 0));
-        points.add(new Point(1, 2));
-        points.add(new Point(2, -20));
-        points.add(new Point(3, 0));
-        points.add(new Point(4, -1));
-        points.add(new Point(5, -1.5));
-        points.add(new Point(6, 0));
-
-        List<Point> points2 = new ArrayList<>();
-//        points2.add(points.get(0));
-//        points2.add(points.get(3));
-//        points2.add(points.get(6));
-        points2.add(new Point(1,-10));
-        points2.add(new Point(3,0));
-
-        double area = total_areal_displacement(points, points2, true);
-        System.out.println("Total area: " + area);
-
-//        points = new ArrayList<>();
-//        points.add(new Point(0, 0));
-//        points.add(new Point(1, 2));
-//        points.add(new Point(1.5, -10));
-//        double area = calculatePolygonArea(points);
-//        System.out.println(area);
-//
-//        Point[] L1 = new Point[2];
-//        L1[0] = new Point(1, 2);
-//        L1[1] = new Point(2, -2);
-//        Point[] L2 = new Point[2];
-//        L2[0] = new Point(0, 0);
-//        L2[1] = new Point(3, 0);
-//        Object[] res = lineIntersection(L1, L2);
-//        System.out.println(res[1]);
-    }
+    return totalArea;
+  }
+
+  // 测试方法
+  public static void main(String[] args) {
+    // 示例数据
+    List<Point> points = new ArrayList<>();
+    points.add(new Point(0, 0));
+    points.add(new Point(1, 2));
+    points.add(new Point(2, -20));
+    points.add(new Point(3, 0));
+    points.add(new Point(4, -1));
+    points.add(new Point(5, -1.5));
+    points.add(new Point(6, 0));
+
+    List<Point> points2 = new ArrayList<>();
+    //        points2.add(points.get(0));
+    //        points2.add(points.get(3));
+    //        points2.add(points.get(6));
+    points2.add(new Point(1, -10));
+    points2.add(new Point(3, 0));
+
+    double area = total_areal_displacement(points, points2, true);
+    System.out.println("Total area: " + area);
+
+    //        points = new ArrayList<>();
+    //        points.add(new Point(0, 0));
+    //        points.add(new Point(1, 2));
+    //        points.add(new Point(1.5, -10));
+    //        double area = calculatePolygonArea(points);
+    //        System.out.println(area);
+    //
+    //        Point[] L1 = new Point[2];
+    //        L1[0] = new Point(1, 2);
+    //        L1[1] = new Point(2, -2);
+    //        Point[] L2 = new Point[2];
+    //        L2[0] = new Point(0, 0);
+    //        L2[1] = new Point(3, 0);
+    //        Object[] res = lineIntersection(L1, L2);
+    //        System.out.println(res[1]);
+  }
 }
diff --git a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Triangle.java 
b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Triangle.java
index 79f7d440c99..b4c52ebfe3f 100644
--- a/server/src/main/java/org/apache/iotdb/db/query/eBUG/Triangle.java
+++ b/server/src/main/java/org/apache/iotdb/db/query/eBUG/Triangle.java
@@ -4,46 +4,46 @@ package org.apache.iotdb.db.query.eBUG;
 // https://github.com/ofZach/Visvalingam-Whyatt/blob/master/src/testApp.cpp
 public class Triangle {
 
-    int[] indices = new int[3];
-    double area;
-    Triangle prev;
-    Triangle next;
-    boolean isDeleted;
-
-    public Triangle(int index1, int index2, int index3, double area) {
-        this.indices[0] = index1;
-        this.indices[1] = index2;
-        this.indices[2] = index3;
-        this.area = area;
-        this.isDeleted = false; // flag for removal. Avoid using 
heap.remove(x) as it is O(n) complexity
+  int[] indices = new int[3];
+  double area;
+  Triangle prev;
+  Triangle next;
+  boolean isDeleted;
+
+  public Triangle(int index1, int index2, int index3, double area) {
+    this.indices[0] = index1;
+    this.indices[1] = index2;
+    this.indices[2] = index3;
+    this.area = area;
+    this.isDeleted = false; // flag for removal. Avoid using heap.remove(x) as 
it is O(n) complexity
+  }
+
+  public Triangle(Triangle oldTri) {
+    // deep copy and inherit connection
+
+    this.indices[0] = oldTri.indices[0];
+    this.indices[1] = oldTri.indices[1];
+    this.indices[2] = oldTri.indices[2];
+    this.area = oldTri.area;
+    this.prev = oldTri.prev;
+    this.next = oldTri.next;
+
+    // TODO important! inherit connection relationship to this new point
+    if (this.prev != null) { // previous point to this new point
+      this.prev.next = this;
     }
-
-    public Triangle(Triangle oldTri) {
-        // deep copy and inherit connection
-
-        this.indices[0] = oldTri.indices[0];
-        this.indices[1] = oldTri.indices[1];
-        this.indices[2] = oldTri.indices[2];
-        this.area = oldTri.area;
-        this.prev = oldTri.prev;
-        this.next = oldTri.next;
-
-        // TODO important! inherit connection relationship to this new point
-        if (this.prev != null) { // previous point to this new point
-            this.prev.next = this;
-        }
-        if (this.next != null) { // next point to this new point
-            this.next.prev = this;
-        }
-
-        this.isDeleted = false; // this new triangle is not deleted
+    if (this.next != null) { // next point to this new point
+      this.next.prev = this;
     }
 
-    public boolean isValid() {
-        return !isDeleted;
-    }
+    this.isDeleted = false; // this new triangle is not deleted
+  }
 
-    public void markDeleted() {
-        this.isDeleted = true;
-    }
+  public boolean isValid() {
+    return !isDeleted;
+  }
+
+  public void markDeleted() {
+    this.isDeleted = true;
+  }
 }
diff --git a/server/src/main/java/org/apache/iotdb/db/query/eBUG/eBUG.java 
b/server/src/main/java/org/apache/iotdb/db/query/eBUG/eBUG.java
index e177b1dcf20..201f99d2313 100644
--- a/server/src/main/java/org/apache/iotdb/db/query/eBUG/eBUG.java
+++ b/server/src/main/java/org/apache/iotdb/db/query/eBUG/eBUG.java
@@ -27,341 +27,390 @@ import java.util.*;
 import static org.apache.iotdb.db.query.eBUG.Tool.total_areal_displacement;
 import static org.apache.iotdb.db.query.eBUG.Tool.triArea;
 
-
 public class eBUG {
-    public static List<Point> findEliminated(Polyline lineToSimplify, int 
pa_idx, int pb_idx) {
-        // pa: left adjacent non-eliminated point of pi
-        // pb: right adjacent non-eliminated point of pi
-        // return a list of points, T'_max{0,k-e}[a:b] order by time in 
ascending order
-
-        // 
性质:最近淘汰的那一个点一定是位于pa~pb之间,因为正是这个点的淘汰才使得pi的significance要更新!至于其他全局更早淘汰的点则不一定位于a:b之间
-        // pa,xxx,pi,xxx,pb
-        // when e=0,遍历点数就是3
-        // when e>0,遍历点数大于等于4、小于等于e+3
-
-        List<Point> res = new ArrayList<>();
-        Point start = lineToSimplify.get(pa_idx);
-        Point end = lineToSimplify.get(pb_idx);
-//        int cnt = 0;
-        while (start != end) { // 
Point类里增加prev&next指针,这样T'_max{0,k-e}里点的连接关系就有了,这样从Pa开始沿着指针,遍历点数一定不超过e+3
-            res.add(start);
-            start = start.next; // when e=0, only traversing three points pa 
pi pb
-//            cnt += 1;
-        }
-        res.add(end);
-//        cnt += 1;
-//        System.out.println(cnt); // 3<=cnt<=e+3
+  public static List<Point> findEliminated(Polyline lineToSimplify, int 
pa_idx, int pb_idx) {
+    // pa: left adjacent non-eliminated point of pi
+    // pb: right adjacent non-eliminated point of pi
+    // return a list of points, T'_max{0,k-e}[a:b] order by time in ascending 
order
+
+    // 
性质:最近淘汰的那一个点一定是位于pa~pb之间,因为正是这个点的淘汰才使得pi的significance要更新!至于其他全局更早淘汰的点则不一定位于a:b之间
+    // pa,xxx,pi,xxx,pb
+    // when e=0,遍历点数就是3
+    // when e>0,遍历点数大于等于4、小于等于e+3
+
+    List<Point> res = new ArrayList<>();
+    Point start = lineToSimplify.get(pa_idx);
+    Point end = lineToSimplify.get(pb_idx);
+    //        int cnt = 0;
+    while (start
+        != end) { // 
Point类里增加prev&next指针,这样T'_max{0,k-e}里点的连接关系就有了,这样从Pa开始沿着指针,遍历点数一定不超过e+3
+      res.add(start);
+      start = start.next; // when e=0, only traversing three points pa pi pb
+      //            cnt += 1;
+    }
+    res.add(end);
+    //        cnt += 1;
+    //        System.out.println(cnt); // 3<=cnt<=e+3
+
+    return res;
+  }
+
+  public static List<Point> buildEffectiveArea(Polyline lineToSimplify, int e, 
boolean debug) {
+    // precomputation mode
+    return buildEffectiveArea(lineToSimplify, e, debug, 0);
+  }
+
+  public static List<Point> buildEffectiveArea(
+      Polyline lineToSimplify, int e, boolean debug, int m) {
+    if (e < 0) {
+      throw new IllegalArgumentException("Parameter e must be non-negative.");
+    }
 
-        return res;
+    if (m > 2) {
+      System.out.println(
+          "online sampling mode, "
+              + "returning "
+              + m
+              + " sampled points sorted by time in ascending order");
+    } else {
+      System.out.println(
+          "offline precomputation mode, "
+              + "returning each point sorted by dominated significance (DS) in 
ascending order");
     }
 
-    public static List<Point> buildEffectiveArea(Polyline lineToSimplify, int 
e, boolean debug) {
-        // precomputation mode
-        return buildEffectiveArea(lineToSimplify, e, debug, 0);
+    //        List<Point> results = lineToSimplify.getVertices(); // 浅复制
+    // TODO 预计算结果改成按照bottom-up逐点淘汰顺序(DS递增)排列而不是按照时间戳,这样省去在线时对DS排序的过程
+    //    add的是Point引用,所以没有多用一倍的空间
+    List<Point> resultsBottomUpEliminated = new ArrayList<>();
+
+    // 存储的是点的引用,这样可以修改原来序列里点的淘汰状态
+    // 存储的是距离当前最新状态的滞后的尚未施加、待施加的e个淘汰点
+    LinkedList<Point> laggedEliminatedPoints = new LinkedList<>();
+
+    int total = lineToSimplify.size();
+    if (total < 3) {
+      return lineToSimplify.getVertices(); // 不足 3 个点无法形成三角形
     }
 
-    public static List<Point> buildEffectiveArea(Polyline lineToSimplify, int 
e, boolean debug, int m) {
-        if (e < 0) {
-            throw new IllegalArgumentException("Parameter e must be 
non-negative.");
-        }
+    int nTriangles = total - 2;
+    Triangle[] triangles = new Triangle[nTriangles];
+
+    // 创建所有三角形并计算初始面积
+    lineToSimplify.get(0).prev = null;
+    lineToSimplify.get(0).next = lineToSimplify.get(1);
+    lineToSimplify.get(total - 1).next = null;
+    lineToSimplify.get(total - 1).prev = lineToSimplify.get(total - 2);
+    for (int i = 1; i < total - 1; i++) {
+      int index1 = i - 1, index2 = i, index3 = i + 1;
+      double area =
+          triArea(
+              lineToSimplify.get(index1), lineToSimplify.get(index2), 
lineToSimplify.get(index3));
+      triangles[i - 1] = new Triangle(index1, index2, index3, area);
+
+      // 初始化点的状态 for eBUG usage
+      lineToSimplify.get(i).prev = lineToSimplify.get(i - 1);
+      lineToSimplify.get(i).next = lineToSimplify.get(i + 1);
+    }
 
-        if (m > 2) {
-            System.out.println("online sampling mode, " +
-                    "returning " + m + " sampled points sorted by time in 
ascending order");
-        } else {
-            System.out.println("offline precomputation mode, " +
-                    "returning each point sorted by dominated significance 
(DS) in ascending order");
+    // 设置三角形的前后关系
+    for (int i = 0; i < nTriangles; i++) { // TODO 这个可以和上一个循环合并吗??好像不可以
+      triangles[i].prev = (i == 0 ? null : triangles[i - 1]);
+      triangles[i].next = (i == nTriangles - 1 ? null : triangles[i + 1]);
+    }
+
+    // 使用优先队列构建 minHeap
+    PriorityQueue<Triangle> triangleHeap =
+        new PriorityQueue<>(Comparator.comparingDouble(t -> t.area));
+    Collections.addAll(triangleHeap, triangles); // complexity TODO O(n) or 
O(nlogn)?
+
+    double previousEA = -1;
+    //        while (!triangleHeap.isEmpty()) { // TODO 
注意triangleHeap里装的是non-terminal point对应的三角形
+    // TODO 在线采样m个点,也就是说最后留下m-2个non-terminal point
+    //      注意:triangleHeap里装的包括了标记删除的点!所以triangleHeap.size()不是真正的留下的未被淘汰点数!
+    //      
因此需要用fakeCnt来统计heap里的非真实点数,这样triangleHeap.size()-fakeCnt就是真正的留下的未被淘汰点数
+    int remainNonTerminalPoint = Math.max(0, m - 2);
+    int fakeCnt = 0;
+    while (triangleHeap.size() - fakeCnt > remainNonTerminalPoint) {
+      // 注意peek只需要直接访问该位置的元素,不涉及任何重排或堆化操作
+      // 而poll是删除堆顶元素,需要重新堆化以维护堆的性质,复杂度是O(logk),k是当前堆的大小
+      Triangle tri = triangleHeap.poll(); // O(logn)
+
+      // 如果该三角形已经被删除,跳过. Avoid using heap.remove(x) as it is O(n) complexity
+      // 而且除了heap里,已经没有其他节点会和它关联了,所有的connections关系已经迁移到新的角色替代节点上
+      if (tri.isDeleted) {
+        fakeCnt--; // 取出了一个被标记删除点
+        if (debug) {
+          System.out.println(
+              ">>>bottom-up, remaining "
+                  + triangleHeap.size()
+                  + " triangles (including those marked for removal)");
+        }
+        continue;
+      }
+
+      // 真正的淘汰点
+      // 记录最近淘汰的点,注意不要重复记录也就是在上面执行之后再确认淘汰
+      if (debug) {
+        System.out.println("(1) eliminate " + 
lineToSimplify.get(tri.indices[1]));
+      }
+      if (e > 0) {
+        if (laggedEliminatedPoints.size() == e) {
+          // 已经有e个滞后淘汰点了,为了把最近淘汰点加入,得先把最老的淘汰点施加上去
+          Point removedPoint = laggedEliminatedPoints.removeFirst(); // 
取出最早加入的淘汰点 复杂度1
+          removedPoint.markEliminated(); // 注意是引用,所以改的内容后面可以看到
+        }
+        laggedEliminatedPoints.addLast(lineToSimplify.get(tri.indices[1])); // 
加入最新的淘汰点,滞后在这里先不施加
+      } else { // e=0 没有滞后 立即标记删除 T'_k
+        lineToSimplify.get(tri.indices[1]).markEliminated();
+      }
+      if (debug) {
+        System.out.println(
+            "the e most recently eliminated points (lagged):" + 
laggedEliminatedPoints);
+      }
+
+      // 更新当前点的重要性(z 轴存储effective area,这是一个单调增的指标)
+      if (tri.area > previousEA) {
+        previousEA = tri.area;
+      }
+      //            results.get(tri.indices[1]).z = previousEA; // dominated 
significance
+      lineToSimplify.get(tri.indices[1]).z = previousEA; // dominated 
significance
+      resultsBottomUpEliminated.add(
+          lineToSimplify.get(tri.indices[1])); // TODO add的是Point引用,所以没有多用一倍的空间
+      if (debug) {
+        System.out.println(Arrays.toString(tri.indices) + ", Dominated Sig=" + 
previousEA);
+      }
+
+      // 更新相邻三角形
+      if (tri.prev != null) {
+        // 
标记为失效点,同时new一个新的对象接管它的一切数据和前后连接关系,然后更新前后连接关系、更新significance、加入heap使其排好序
+
+        // 1. 处理旧的tri.prev被标记删除的事情(角色替代)
+        // triangleHeap.remove(tri.prev); // Avoid using heap.remove(x) as it 
is O(n) complexity!
+        tri.prev.markDeleted(); // O(1) 
这个点标记为废掉,前后关联都砍断,但是不remove因为那太耗时,只要heap poll到它就跳过就可以
+
+        Triangle newPre = new Triangle(tri.prev); // deep copy and inherit 
connection
+        // tri.prev = newPre; // can omit, because already done by new 
Triangle(tri.prev)
+
+        // 2. 处理pi被淘汰引起tri.prev被更新的事情
+        // 前一个三角形连到后一个三角形
+        tri.prev.next =
+            tri.next; // ATTENTION!!!: 
这里的tri.next后面可能会因为处理旧的tri.next被标记删除的事情被换掉!到时候要重新赋值!
+        tri.prev.indices[2] = tri.indices[2];
+
+        // e parameter
+        List<Point> pointsForSig =
+            findEliminated(lineToSimplify, tri.prev.indices[0], 
tri.prev.indices[2]);
+        if (debug) {
+          System.out.println(
+              "(2) update point on the left " + 
lineToSimplify.get(tri.prev.indices[1]));
+          System.out.println("3<=cnt<=e+3. cnt=" + pointsForSig.size());
+          for (Point point : pointsForSig) {
+            System.out.println("\t" + point);
+          }
+        }
+        List<Point> baseLine = new ArrayList<>();
+        baseLine.add(pointsForSig.get(0));
+        baseLine.add(pointsForSig.get(pointsForSig.size() - 1)); // 
直接连接左右两边最近的未被淘汰的点
+        double sig = total_areal_displacement(pointsForSig, baseLine, false);
+        tri.prev.area = sig;
+
+        if (debug) {
+          System.out.println("sig=" + sig);
+          double tmpTri =
+              triArea(
+                  lineToSimplify.get(tri.prev.indices[0]),
+                  lineToSimplify.get(tri.prev.indices[1]),
+                  lineToSimplify.get(tri.prev.indices[2]));
+          System.out.println(
+              "\t"
+                  + "tri="
+                  + tmpTri
+                  + ", "
+                  + ((tmpTri > sig) ? "over-estimated" : 
"equal/less-estimated"));
         }
 
-//        List<Point> results = lineToSimplify.getVertices(); // 浅复制
-        // TODO 预计算结果改成按照bottom-up逐点淘汰顺序(DS递增)排列而不是按照时间戳,这样省去在线时对DS排序的过程
-        //    add的是Point引用,所以没有多用一倍的空间
-        List<Point> resultsBottomUpEliminated = new ArrayList<>();
+        // 重新加入堆
+        // 在 Java 的 PriorityQueue 中,修改元素的属性不会自动更新堆的顺序
+        // 所以必须通过add来显式重新插入修改后的元素
+        triangleHeap.add(tri.prev); // O(logn) 注意加入的是一个新的对象isDeleted=false
+        fakeCnt++; // 表示heap里多了一个被标记删除的假点
+      }
 
-        // 存储的是点的引用,这样可以修改原来序列里点的淘汰状态
-        // 存储的是距离当前最新状态的滞后的尚未施加、待施加的e个淘汰点
-        LinkedList<Point> laggedEliminatedPoints = new LinkedList<>();
+      if (tri.next != null) {
+        // 
标记为失效点,同时new一个新的对象接管它的一切数据和前后连接关系,然后更新前后连接关系、更新significance、加入heap使其排好序
 
-        int total = lineToSimplify.size();
-        if (total < 3) {
-            return lineToSimplify.getVertices(); // 不足 3 个点无法形成三角形
-        }
+        // 1. 处理旧的tri.next被标记删除的事情(角色替代)
+        // triangleHeap.remove(tri.next); // Avoid using heap.remove(x) as it 
is O(n) complexity
+        tri.next.markDeleted(); // O(1) 
这个点标记为废掉,前后关联都砍断,但是不remove因为那太耗时,只有poll到它就跳过就可以
 
-        int nTriangles = total - 2;
-        Triangle[] triangles = new Triangle[nTriangles];
-
-        // 创建所有三角形并计算初始面积
-        lineToSimplify.get(0).prev = null;
-        lineToSimplify.get(0).next = lineToSimplify.get(1);
-        lineToSimplify.get(total - 1).next = null;
-        lineToSimplify.get(total - 1).prev = lineToSimplify.get(total - 2);
-        for (int i = 1; i < total - 1; i++) {
-            int index1 = i - 1, index2 = i, index3 = i + 1;
-            double area = triArea(lineToSimplify.get(index1), 
lineToSimplify.get(index2), lineToSimplify.get(index3));
-            triangles[i - 1] = new Triangle(index1, index2, index3, area);
-
-            // 初始化点的状态 for eBUG usage
-            lineToSimplify.get(i).prev = lineToSimplify.get(i - 1);
-            lineToSimplify.get(i).next = lineToSimplify.get(i + 1);
-        }
+        Triangle newNext = new Triangle(tri.next); // deep copy and inherit 
connection
+        // tri.next = newNext; // omit, because already done by new 
Triangle(tri.prev)
 
-        // 设置三角形的前后关系
-        for (int i = 0; i < nTriangles; i++) { // TODO 这个可以和上一个循环合并吗??好像不可以
-            triangles[i].prev = (i == 0 ? null : triangles[i - 1]);
-            triangles[i].next = (i == nTriangles - 1 ? null : triangles[i + 
1]);
+        if (tri.prev != null) {
+          tri.prev.next = tri.next; // ATTENTION!!!: 
这里的tri.next已经被换掉!所以之前的要重新赋值!
         }
 
-        // 使用优先队列构建 minHeap
-        PriorityQueue<Triangle> triangleHeap = new 
PriorityQueue<>(Comparator.comparingDouble(t -> t.area));
-        Collections.addAll(triangleHeap, triangles); // complexity TODO O(n) 
or O(nlogn)?
-
-        double previousEA = -1;
-//        while (!triangleHeap.isEmpty()) { // TODO 
注意triangleHeap里装的是non-terminal point对应的三角形
-        // TODO 在线采样m个点,也就是说最后留下m-2个non-terminal point
-        //      
注意:triangleHeap里装的包括了标记删除的点!所以triangleHeap.size()不是真正的留下的未被淘汰点数!
-        //      
因此需要用fakeCnt来统计heap里的非真实点数,这样triangleHeap.size()-fakeCnt就是真正的留下的未被淘汰点数
-        int remainNonTerminalPoint = Math.max(0, m - 2);
-        int fakeCnt = 0;
-        while (triangleHeap.size() - fakeCnt > remainNonTerminalPoint) {
-            // 注意peek只需要直接访问该位置的元素,不涉及任何重排或堆化操作
-            // 而poll是删除堆顶元素,需要重新堆化以维护堆的性质,复杂度是O(logk),k是当前堆的大小
-            Triangle tri = triangleHeap.poll(); // O(logn)
-
-            // 如果该三角形已经被删除,跳过. Avoid using heap.remove(x) as it is O(n) 
complexity
-            // 而且除了heap里,已经没有其他节点会和它关联了,所有的connections关系已经迁移到新的角色替代节点上
-            if (tri.isDeleted) {
-                fakeCnt--; // 取出了一个被标记删除点
-                if (debug) {
-                    System.out.println(">>>bottom-up, remaining " + 
triangleHeap.size() + " triangles (including those marked for removal)");
-                }
-                continue;
-            }
-
-            // 真正的淘汰点
-            // 记录最近淘汰的点,注意不要重复记录也就是在上面执行之后再确认淘汰
-            if (debug) {
-                System.out.println("(1) eliminate " + 
lineToSimplify.get(tri.indices[1]));
-            }
-            if (e > 0) {
-                if (laggedEliminatedPoints.size() == e) {
-                    // 已经有e个滞后淘汰点了,为了把最近淘汰点加入,得先把最老的淘汰点施加上去
-                    Point removedPoint = laggedEliminatedPoints.removeFirst(); 
// 取出最早加入的淘汰点 复杂度1
-                    removedPoint.markEliminated(); // 注意是引用,所以改的内容后面可以看到
-                }
-                
laggedEliminatedPoints.addLast(lineToSimplify.get(tri.indices[1])); // 
加入最新的淘汰点,滞后在这里先不施加
-            } else { // e=0 没有滞后 立即标记删除 T'_k
-                lineToSimplify.get(tri.indices[1]).markEliminated();
-            }
-            if (debug) {
-                System.out.println("the e most recently eliminated points 
(lagged):" + laggedEliminatedPoints);
-            }
-
-            // 更新当前点的重要性(z 轴存储effective area,这是一个单调增的指标)
-            if (tri.area > previousEA) {
-                previousEA = tri.area;
-            }
-//            results.get(tri.indices[1]).z = previousEA; // dominated 
significance
-            lineToSimplify.get(tri.indices[1]).z = previousEA; // dominated 
significance
-            resultsBottomUpEliminated.add(lineToSimplify.get(tri.indices[1])); 
// TODO add的是Point引用,所以没有多用一倍的空间
-            if (debug) {
-                System.out.println(Arrays.toString(tri.indices) + ", Dominated 
Sig=" + previousEA);
-            }
-
-            // 更新相邻三角形
-            if (tri.prev != null) {
-                // 
标记为失效点,同时new一个新的对象接管它的一切数据和前后连接关系,然后更新前后连接关系、更新significance、加入heap使其排好序
-
-                // 1. 处理旧的tri.prev被标记删除的事情(角色替代)
-                // triangleHeap.remove(tri.prev); // Avoid using 
heap.remove(x) as it is O(n) complexity!
-                tri.prev.markDeleted(); // O(1) 
这个点标记为废掉,前后关联都砍断,但是不remove因为那太耗时,只要heap poll到它就跳过就可以
-
-                Triangle newPre = new Triangle(tri.prev); // deep copy and 
inherit connection
-                // tri.prev = newPre; // can omit, because already done by new 
Triangle(tri.prev)
-
-                // 2. 处理pi被淘汰引起tri.prev被更新的事情
-                // 前一个三角形连到后一个三角形
-                tri.prev.next = tri.next; // ATTENTION!!!: 
这里的tri.next后面可能会因为处理旧的tri.next被标记删除的事情被换掉!到时候要重新赋值!
-                tri.prev.indices[2] = tri.indices[2];
-
-                // e parameter
-                List<Point> pointsForSig = findEliminated(lineToSimplify, 
tri.prev.indices[0], tri.prev.indices[2]);
-                if (debug) {
-                    System.out.println("(2) update point on the left " + 
lineToSimplify.get(tri.prev.indices[1]));
-                    System.out.println("3<=cnt<=e+3. cnt=" + 
pointsForSig.size());
-                    for (Point point : pointsForSig) {
-                        System.out.println("\t" + point);
-                    }
-                }
-                List<Point> baseLine = new ArrayList<>();
-                baseLine.add(pointsForSig.get(0));
-                baseLine.add(pointsForSig.get(pointsForSig.size() - 1)); // 
直接连接左右两边最近的未被淘汰的点
-                double sig = total_areal_displacement(pointsForSig, baseLine, 
false);
-                tri.prev.area = sig;
-
-                if (debug) {
-                    System.out.println("sig=" + sig);
-                    double tmpTri = 
triArea(lineToSimplify.get(tri.prev.indices[0]),
-                            lineToSimplify.get(tri.prev.indices[1]),
-                            lineToSimplify.get(tri.prev.indices[2]));
-                    System.out.println("\t" + "tri=" + tmpTri + ", " + 
((tmpTri > sig) ? "over-estimated" : "equal/less-estimated"));
-                }
-
-                // 重新加入堆
-                // 在 Java 的 PriorityQueue 中,修改元素的属性不会自动更新堆的顺序
-                // 所以必须通过add来显式重新插入修改后的元素
-                triangleHeap.add(tri.prev); // O(logn) 
注意加入的是一个新的对象isDeleted=false
-                fakeCnt++; // 表示heap里多了一个被标记删除的假点
-            }
-
-            if (tri.next != null) {
-                // 
标记为失效点,同时new一个新的对象接管它的一切数据和前后连接关系,然后更新前后连接关系、更新significance、加入heap使其排好序
-
-                // 1. 处理旧的tri.next被标记删除的事情(角色替代)
-                // triangleHeap.remove(tri.next); // Avoid using 
heap.remove(x) as it is O(n) complexity
-                tri.next.markDeleted(); // O(1) 
这个点标记为废掉,前后关联都砍断,但是不remove因为那太耗时,只有poll到它就跳过就可以
-
-                Triangle newNext = new Triangle(tri.next); // deep copy and 
inherit connection
-                // tri.next = newNext; // omit, because already done by new 
Triangle(tri.prev)
-
-                if (tri.prev != null) {
-                    tri.prev.next = tri.next; // ATTENTION!!!: 
这里的tri.next已经被换掉!所以之前的要重新赋值!
-                }
-
-                // 2. 处理pi被淘汰引起tri.next被更新的事情
-                tri.next.prev = tri.prev; // 
注意此时tri.prev已经是替代后的节点,tri.next也是,从而被标记为废点的前后关联真正砍断
-                tri.next.indices[0] = tri.indices[0];
-
-                // e parameter
-                List<Point> pointsForSig = findEliminated(lineToSimplify, 
tri.next.indices[0], tri.next.indices[2]);
-                if (debug) {
-                    System.out.println("(2) updating point on the right " + 
lineToSimplify.get(tri.next.indices[1]));
-                    System.out.println("3<=cnt<=e+3. cnt=" + 
pointsForSig.size());
-                    for (Point point : pointsForSig) {
-                        System.out.println("\t" + point);
-                    }
-                }
-                List<Point> baseLine = new ArrayList<>();
-                baseLine.add(pointsForSig.get(0));
-                baseLine.add(pointsForSig.get(pointsForSig.size() - 1)); // 
直接连接左右两边最近的未被淘汰的点
-                double sig = total_areal_displacement(pointsForSig, baseLine, 
false);
-                tri.next.area = sig;
-
-                if (debug) {
-                    System.out.println("sig=" + sig);
-                    double tmpTri = 
triArea(lineToSimplify.get(tri.next.indices[0]),
-                            lineToSimplify.get(tri.next.indices[1]),
-                            lineToSimplify.get(tri.next.indices[2]));
-                    System.out.println("\t" + "tri=" + tmpTri + ", " + 
((tmpTri > sig) ? "over-estimated" : "equal/less-estimated"));
-                }
-
-                // 重新加入堆
-                // 在 Java 的 PriorityQueue 中,修改元素的属性不会自动更新堆的顺序
-                // 所以必须通过add 来显式重新插入修改后的元素
-                triangleHeap.add(tri.next); // 注意加入的是一个新的对象isDeleted=false
-                fakeCnt++; // 表示heap里多了一个被标记删除的假点
-            }
-            if (debug) {
-                System.out.println(">>>bottom-up, remaining " + 
triangleHeap.size() + " triangles (including those marked for removal)");
-            }
+        // 2. 处理pi被淘汰引起tri.next被更新的事情
+        tri.next.prev = tri.prev; // 
注意此时tri.prev已经是替代后的节点,tri.next也是,从而被标记为废点的前后关联真正砍断
+        tri.next.indices[0] = tri.indices[0];
+
+        // e parameter
+        List<Point> pointsForSig =
+            findEliminated(lineToSimplify, tri.next.indices[0], 
tri.next.indices[2]);
+        if (debug) {
+          System.out.println(
+              "(2) updating point on the right " + 
lineToSimplify.get(tri.next.indices[1]));
+          System.out.println("3<=cnt<=e+3. cnt=" + pointsForSig.size());
+          for (Point point : pointsForSig) {
+            System.out.println("\t" + point);
+          }
         }
-
-        if (m > 2) { // online sampling mode
-            // 把滞后的淘汰点施加上去,然后返回在线采样结果(也就是返回剩余未被淘汰的点)
-            for (Point p : laggedEliminatedPoints) {
-                p.markEliminated();
-                if (debug) {
-                    System.out.println("apply lagged elimination of " + p);
-                }
-            }
-            List<Point> onlineSampled = new ArrayList<>();
-            Point start = lineToSimplify.get(0);
-            Point end = lineToSimplify.get(lineToSimplify.size() - 1);
-            while (start != end) { // 
Point类里增加prev&next指针,这样T'_max{0,k-e}里点的连接关系就有了,这样从Pa开始沿着指针,遍历点数一定不超过e+3
-                onlineSampled.add(start); // 注意未淘汰的点的Dominated 
significance尚未赋值,还都是infinity
-                start = start.next; // when e=0, only traversing three points 
pa pi pb
-            }
-            onlineSampled.add(end);
-            return onlineSampled;
-        } else { // offline precomputation mode, for precomputing the 
dominated significance of each point
-//            return results; // 注意这就是lineToSimplify.getVertices()
-            // TODO
-            resultsBottomUpEliminated.add(lineToSimplify.get(0)); // 全局首点
-            
resultsBottomUpEliminated.add(lineToSimplify.get(lineToSimplify.size() - 1)); 
// 全局尾点
-            return resultsBottomUpEliminated;
+        List<Point> baseLine = new ArrayList<>();
+        baseLine.add(pointsForSig.get(0));
+        baseLine.add(pointsForSig.get(pointsForSig.size() - 1)); // 
直接连接左右两边最近的未被淘汰的点
+        double sig = total_areal_displacement(pointsForSig, baseLine, false);
+        tri.next.area = sig;
+
+        if (debug) {
+          System.out.println("sig=" + sig);
+          double tmpTri =
+              triArea(
+                  lineToSimplify.get(tri.next.indices[0]),
+                  lineToSimplify.get(tri.next.indices[1]),
+                  lineToSimplify.get(tri.next.indices[2]));
+          System.out.println(
+              "\t"
+                  + "tri="
+                  + tmpTri
+                  + ", "
+                  + ((tmpTri > sig) ? "over-estimated" : 
"equal/less-estimated"));
         }
+
+        // 重新加入堆
+        // 在 Java 的 PriorityQueue 中,修改元素的属性不会自动更新堆的顺序
+        // 所以必须通过add 来显式重新插入修改后的元素
+        triangleHeap.add(tri.next); // 注意加入的是一个新的对象isDeleted=false
+        fakeCnt++; // 表示heap里多了一个被标记删除的假点
+      }
+      if (debug) {
+        System.out.println(
+            ">>>bottom-up, remaining "
+                + triangleHeap.size()
+                + " triangles (including those marked for removal)");
+      }
     }
 
-    public static void main(String[] args) {
-
-//        int eParam = 0;
-//        int[] eParamList = {0, 0, 1, 2, 3, 4, 5, 10, 14, 15, 16, 20, 30, 40, 
50, 100, 200, 500, 1000, 2000, 5000,
-//                10000, 50000, 10_0000, 50_0000, 100_0000, 200_0000, 300_0000,
-//                500_0000, 800_0000, 1000_0000,
-//                1500_0000, 2000_0000, 2500_0000, 3000_0000};
-        int[] eParamList = {100_0000};
-        for (int eParam : eParamList) {
-            try (PrintWriter writer = new PrintWriter(new File("exp_varyN_e" + 
eParam + ".csv"))) {
-                for (int n = 100_0000; n < 2000_0000; n += 200_0000) { // 
超过两千万就都变得慢多了,感觉可能是内存有限的原因,而不是算法复杂度
-                    // TODO 注意 要有一个点是n=300w
-
-                    Polyline polyline = new Polyline();
-                    int seed = 1;
-                    Random rand = new Random(seed); // TODO 注意seed在每轮里重设
-                    for (int i = 0; i < n; i++) {
-                        double v = rand.nextInt(1000000);
-                        polyline.addVertex(new Point(i, v));
-                    }
-
-                    long startTime = System.currentTimeMillis();
-                    List<Point> results = buildEffectiveArea(polyline, eParam, 
false, 0);
-                    long endTime = System.currentTimeMillis();
-
-                    System.out.println("n=" + n + ", e=" + eParam + ", Time 
taken to reduce points: " + (endTime - startTime) + "ms");
-                    writer.println(n + "," + eParam + "," + (endTime - 
startTime));
-                    System.out.println(results.size());
-
-//                // clear
-//                polyline.clear();
-//                results.clear();
-//                polyline = null;
-//                results = null;
-//                System.gc();
-                }
-            } catch (FileNotFoundException e) {
-                throw new RuntimeException(e);
-            }
+    if (m > 2) { // online sampling mode
+      // 把滞后的淘汰点施加上去,然后返回在线采样结果(也就是返回剩余未被淘汰的点)
+      for (Point p : laggedEliminatedPoints) {
+        p.markEliminated();
+        if (debug) {
+          System.out.println("apply lagged elimination of " + p);
         }
-
-//        int n = 300_0000;
-//
-//        int seed = 1;
-//        Random rand = new Random(seed); // TODO 注意seed在每轮里重设
-//        Polyline polyline = new Polyline(); // 
注意:如果是固定n变化e实验,这个数据要一次性生成,不然每次随机不一样
-//        for (int i = 0; i < n; i++) {
-//            double v = rand.nextInt(1000000);
-//            polyline.addVertex(new Point(i, v)); // 
point的状态会在buildEffectiveArea里重置的,所以在下面的e遍历里可以复用这一份数据
-//        }
-//
-//        try (PrintWriter writer = new PrintWriter(new File("exp_varyE_n" + n 
+ ".csv"))) {
-//            int[] eParamList = {0, 1, 2, 10, 1000, 10000, 10_0000, 30_0000, 
50_0000, 60_0000, 80_0000, 100_0000, 150_0000, 200_0000};
-//            for (int eParam : eParamList) {
-//                eParam *= 3; // TODO 注意 因为n=300w而不是100w
-//
-//                long startTime = System.currentTimeMillis();
-//                List<Point> results = buildEffectiveArea(polyline, eParam, 
false);
-//                long endTime = System.currentTimeMillis();
-//
-//                System.out.println("n=" + n + ", e=" + eParam + ", Time 
taken to reduce points: " + (endTime - startTime) + "ms");
-//                writer.println(n + "," + eParam + "," + (endTime - 
startTime));
-//                System.out.println(results.size());
-//
-//                // clear 注意不能把原始数据清除,还要接着用
-////                System.gc();
-//            }
-//        } catch (FileNotFoundException e) {
-//            throw new RuntimeException(e);
-//        }
-
-        System.out.println("finish");
+      }
+      List<Point> onlineSampled = new ArrayList<>();
+      Point start = lineToSimplify.get(0);
+      Point end = lineToSimplify.get(lineToSimplify.size() - 1);
+      while (start
+          != end) { // 
Point类里增加prev&next指针,这样T'_max{0,k-e}里点的连接关系就有了,这样从Pa开始沿着指针,遍历点数一定不超过e+3
+        onlineSampled.add(start); // 注意未淘汰的点的Dominated 
significance尚未赋值,还都是infinity
+        start = start.next; // when e=0, only traversing three points pa pi pb
+      }
+      onlineSampled.add(end);
+      return onlineSampled;
+    } else { // offline precomputation mode, for precomputing the dominated 
significance of each
+      // point
+      //            return results; // 注意这就是lineToSimplify.getVertices()
+      // TODO
+      resultsBottomUpEliminated.add(lineToSimplify.get(0)); // 全局首点
+      resultsBottomUpEliminated.add(lineToSimplify.get(lineToSimplify.size() - 
1)); // 全局尾点
+      return resultsBottomUpEliminated;
     }
+  }
+
+  public static void main(String[] args) {
+    // 实验:预计算耗时关于两个参数e、n的变化规律,是否符合复杂度理论建模
+
+    //        int eParam = 0;
+    //        int[] eParamList = {0, 0, 1, 2, 3, 4, 5, 10, 14, 15, 16, 20, 30, 
40, 50, 100, 200,
+    // 500, 1000, 2000, 5000,
+    //                10000, 50000, 10_0000, 50_0000, 100_0000, 200_0000, 
300_0000,
+    //                500_0000, 800_0000, 1000_0000,
+    //                1500_0000, 2000_0000, 2500_0000, 3000_0000};
+    int[] eParamList = {100_0000};
+    for (int eParam : eParamList) {
+      try (PrintWriter writer = new PrintWriter(new File("exp_varyN_e" + 
eParam + ".csv"))) {
+        for (int n = 100_0000; n < 2000_0000; n += 200_0000) { // 
超过两千万就都变得慢多了,感觉可能是内存有限的原因,而不是算法复杂度
+          // TODO 注意 要有一个点是n=300w
+
+          Polyline polyline = new Polyline();
+          int seed = 1;
+          Random rand = new Random(seed); // TODO 注意seed在每轮里重设
+          for (int i = 0; i < n; i++) {
+            double v = rand.nextInt(1000000);
+            polyline.addVertex(new Point(i, v));
+          }
+
+          long startTime = System.currentTimeMillis();
+          List<Point> results = buildEffectiveArea(polyline, eParam, false, 0);
+          long endTime = System.currentTimeMillis();
+
+          System.out.println(
+              "n="
+                  + n
+                  + ", e="
+                  + eParam
+                  + ", Time taken to reduce points: "
+                  + (endTime - startTime)
+                  + "ms");
+          writer.println(n + "," + eParam + "," + (endTime - startTime));
+          System.out.println(results.size());
+
+          //                // clear
+          //                polyline.clear();
+          //                results.clear();
+          //                polyline = null;
+          //                results = null;
+          //                System.gc();
+        }
+      } catch (FileNotFoundException e) {
+        throw new RuntimeException(e);
+      }
+    }
+
+    //        int n = 300_0000;
+    //
+    //        int seed = 1;
+    //        Random rand = new Random(seed); // TODO 注意seed在每轮里重设
+    //        Polyline polyline = new Polyline(); // 
注意:如果是固定n变化e实验,这个数据要一次性生成,不然每次随机不一样
+    //        for (int i = 0; i < n; i++) {
+    //            double v = rand.nextInt(1000000);
+    //            polyline.addVertex(new Point(i, v)); //
+    // point的状态会在buildEffectiveArea里重置的,所以在下面的e遍历里可以复用这一份数据
+    //        }
+    //
+    //        try (PrintWriter writer = new PrintWriter(new File("exp_varyE_n" 
+ n + ".csv"))) {
+    //            int[] eParamList = {0, 1, 2, 10, 1000, 10000, 10_0000, 
30_0000, 50_0000, 60_0000,
+    // 80_0000, 100_0000, 150_0000, 200_0000};
+    //            for (int eParam : eParamList) {
+    //                eParam *= 3; // TODO 注意 因为n=300w而不是100w
+    //
+    //                long startTime = System.currentTimeMillis();
+    //                List<Point> results = buildEffectiveArea(polyline, 
eParam, false);
+    //                long endTime = System.currentTimeMillis();
+    //
+    //                System.out.println("n=" + n + ", e=" + eParam + ", Time 
taken to reduce
+    // points: " + (endTime - startTime) + "ms");
+    //                writer.println(n + "," + eParam + "," + (endTime - 
startTime));
+    //                System.out.println(results.size());
+    //
+    //                // clear 注意不能把原始数据清除,还要接着用
+    ////                System.gc();
+    //            }
+    //        } catch (FileNotFoundException e) {
+    //            throw new RuntimeException(e);
+    //        }
+
+    System.out.println("finish");
+  }
 }
diff --git 
a/server/src/main/java/org/apache/iotdb/db/query/eBUG/eBUG_Build.java 
b/server/src/main/java/org/apache/iotdb/db/query/eBUG/eBUG_Build.java
new file mode 100644
index 00000000000..94713f71ec8
--- /dev/null
+++ b/server/src/main/java/org/apache/iotdb/db/query/eBUG/eBUG_Build.java
@@ -0,0 +1,139 @@
+package org.apache.iotdb.db.query.eBUG;
+
+import java.io.BufferedWriter;
+import java.io.FileWriter;
+import java.io.IOException;
+import java.nio.file.Files;
+import java.nio.file.Path;
+import java.nio.file.Paths;
+import java.util.Iterator;
+import java.util.List;
+import java.util.stream.Stream;
+
+import static org.apache.iotdb.db.query.eBUG.eBUG.buildEffectiveArea;
+
+public class eBUG_Build {
+  // 输入一条时间序列 t,v
+  // 输出按照bottom-up淘汰顺序排列的dominated significance,t,v。
+  // 用于后期在线采样时选取倒数m个点(也就是DS最大的m个点,或者最晚淘汰的m个点)作为采样结果(选出之后要自行把这m个点重新按照时间戳x递增排列)
+  public static void main(String[] args) {
+    if (args.length < 5) {
+      System.out.println(
+          "Usage: Please provide arguments: 
inputFilePath,hasHeader,timeIdx,valueIdx,eParam,(outDir)");
+    }
+    String input = args[0];
+    boolean hasHeader = Boolean.parseBoolean(args[1]);
+    int timeIdx = Integer.parseInt(args[2]);
+    int valueIdx = Integer.parseInt(args[3]);
+    int eParam = Integer.parseInt(args[4]);
+    String outDir;
+    if (args.length > 5) {
+      outDir = args[5]; // 表示输出文件保存到指定的文件夹
+    } else {
+      outDir = null; // 表示输出文件保存到input文件所在的文件夹
+    }
+    String outputFile = generateOutputFileName(input, eParam, outDir);
+
+    // 打印信息供用户确认
+    System.out.println("Input file: " + input);
+    System.out.println("Has header: " + hasHeader);
+    System.out.println("Time index: " + timeIdx);
+    System.out.println("Value index: " + valueIdx);
+    System.out.println("eParam: " + eParam);
+    System.out.println("outDir: " + outDir);
+    System.out.println("Output file: " + outputFile);
+
+    // 开始运算
+    Polyline polyline = new Polyline();
+
+    // Using Files.lines() for memory-efficient line-by-line reading
+    try (Stream<String> lines = Files.lines(Paths.get(input))) {
+      Iterator<String> iterator = lines.iterator();
+      int lineNumber = 0;
+
+      // Skip the header line if necessary
+      if (hasHeader && iterator.hasNext()) {
+        iterator.next(); // Skip the header
+      }
+
+      // Process each line
+      while (iterator.hasNext()) {
+        lineNumber++;
+        String line = iterator.next();
+        String[] columns = line.split(",");
+
+        if (columns.length > Math.max(timeIdx, valueIdx)) {
+          double time;
+          if (timeIdx < 0) {
+            time = lineNumber;
+          } else {
+            time = Double.parseDouble(columns[timeIdx]);
+          }
+          double value = Double.parseDouble(columns[valueIdx]);
+          polyline.addVertex(new Point(time, value));
+          //                    System.out.println("Line " + lineNumber + " - 
Time: " + time + ",
+          // Value: " + value);
+        } else {
+          System.out.println("Line " + lineNumber + " is malformed (not enough 
columns).");
+        }
+      }
+    } catch (IOException e) {
+      e.printStackTrace();
+    }
+
+    long startTime = System.currentTimeMillis();
+    List<Point> results = buildEffectiveArea(polyline, eParam, false); // 
precomputation mode
+    long endTime = System.currentTimeMillis();
+
+    //        System.out.println("result point number: " + results.size()); // 
precomputation
+    // mode所以自然是等于n个点
+    System.out.println(
+        "n="
+            + polyline.getVertices().size()
+            + ", e="
+            + eParam
+            + ", Time taken to reduce points: "
+            + (endTime - startTime)
+            + "ms");
+
+    // 输出结果到csv,按照z,x,y三列,因为results结果已经按照z(即DS)递增排序,对应bottom-up的淘汰顺序,越小代表越早被淘汰
+    try (BufferedWriter writer = new BufferedWriter(new 
FileWriter(outputFile))) {
+      // 写入表头
+      writer.write("z,x,y");
+      writer.newLine();
+
+      // 写入数据行,按顺序 z, x, y
+      for (Point point : results) {
+        writer.write(point.z + "," + point.x + "," + point.y);
+        writer.newLine();
+      }
+
+      System.out.println("CSV file written successfully to " + outputFile);
+    } catch (IOException e) {
+      e.printStackTrace();
+    }
+  }
+
+  // Method to generate the output file name based on input path
+  private static String generateOutputFileName(String inputFilePath, int e, 
String outDir) {
+    // Get the file name without extension
+    Path path = Paths.get(inputFilePath);
+    String fileNameWithoutExtension = path.getFileName().toString();
+    String name = fileNameWithoutExtension.substring(0, 
fileNameWithoutExtension.lastIndexOf('.'));
+
+    // Get the file extension
+    String extension =
+        
path.getFileName().toString().substring(fileNameWithoutExtension.lastIndexOf('.'));
+
+    // Create output file path by appending '-ds' before the extension
+    String outputFile = name + "-ds-e" + e + extension;
+
+    if (outDir == null) { // 表示使用input文件所在的文件夹
+      // Handle path compatibility for different operating systems 
(Linux/Windows)
+      return path.getParent().resolve(outputFile).toString();
+    } else {
+      Path out = Paths.get(outDir);
+      return out.resolve(outputFile).toString();
+    }
+  }
+}

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