On 02/03/2020 22:34, Claude Warren wrote:
So what we have then is:
*public* *interface* BloomFilter {
*int* andCardinality(BloomFilter other);
*int* cardinality();
*boolean* contains(BloomFilter other);
*boolean* contains(Hasher hasher);
*long*[] getBits();
// Change
PrimitiveIterator.OfInt iterator();
Shape getShape();
* // Change boolean* merge(BloomFilter other);
*// Change boolean* merge(Hasher hasher);
*int* orCardinality(BloomFilter other);
*int* xorCardinality(BloomFilter other);
}
public interface BitCountConsumer {
boolean accept(int index, int count);
}
public interface CountingBloomFilter extends BloomFilter {
*// Change boolean* remove(BloomFilter other);
// Change
*boolean* remove(Hasher hasher);
// Change
boolean add(CountingBloomFilter other);
// Change
boolean subtract(CountingBloomFilter other);
// Change
void getCounts(BitCountConsumer consumer);
}
*public* *final* *class* StaticHasher *implements* Hasher {
*public* StaticHasher(*final* Hasher hasher, *final* Shape shape) { ...
}
*public* StaticHasher(*final* Iterator<Integer> iter, *final* Shape
shape) { ... }
*public* StaticHasher(*final* Collection<Integer> collection, *final*
Shape shape) { ... }
*public* Shape getShape() { *... *}
*public* *int* size() { *... *}
*// Change public* *int* max() { *... *}
}
*public* *final* *class* FixedHasher *implements* Hasher {
*public* FixedHasher(*final* Hasher hasher, *final* Shape shape) { ... }
*public* FixedHasher(*final* Iterator<Integer> iter, *final* Shape shape)
{ ... }
*public* FixedHasher(*final* Collection<Integer> collection, *final*
Shape shape) { ... }
*public* Shape getShape() { *... *}
*public* *int* size() { *... *}
*public* *int* max() { *... *}
}
I have a pull request in to add a CachingHasher.
While we are at it, I think we should change Hasher.getBits(Shape) to
Hasher.iterator(Shape) to match the BloomFilter.iterator() and to limit
confusion between Hasher.getBits( Shape ) (return iterator) and
BloomFilter.getBits() returns (long[])
The interface changes look good to me. I agree with your implementation
ideas.
I do have one use case where I need the BloomFilter.iterator() results in
reverse order (I am estimating Log2 of the filter), but I can do that with
the methods here. I don't think any of these changes significantly impacts
the uses that I currently have.
Shall we move forward?
Claude
I finished a first draft of the CountingBloomFilter. I still have the
tests to add for the new API.
When working with this I had to write an Iterator (to create a Hasher
for the soon to be changed API) which has very few lines of code, most
of which are repeats due to the separation of hasNext() and nextInt()
and the requirement to be able to call hasNext() repeatedly without
calling nextInt(). This mandates storing the next value rather than a
current position to search for a non-zero index:
static class IndexIterator implements PrimitiveIterator.OfInt {
int next;
IndexIterator() {
advance(0);
}
private void advance(int from) {
next = from;
while (next < counts.length && counts[next] == 0) {
next++;
}
}
@Override
public boolean hasNext() {
return next < counts.length;
}
@Override
public int nextInt() {
if (hasNext()) {
final int result = next;
advance(next + 1);
return result;
}
throw new NoSuchElementException();
}
}
This is noted in the Spliterator javadoc:
* <p>Spliterators, like {@code Iterator}s, are for traversing the
elements of
* a source. The {@code Spliterator} API was designed to support efficient
* parallel traversal in addition to sequential traversal, by supporting
* decomposition as well as single-element iteration. In addition, the
* protocol for accessing elements via a Spliterator is designed to impose
* smaller per-element overhead than {@code Iterator}, and to avoid the
inherent
* race involved in having separate methods for {@code hasNext()} and
* {@code next()}.
The same code written as a Spliterator has a much simpler tryAdvance
method with only a single comparison of the current index to the upper
limit per access of each element.
static class IndexSpliterator implements Spliterator.OfInt {
int index;
@Override
public long estimateSize() {
return Long.MAX_VALUE;
}
@Override
public int characteristics() {
return Spliterator.SORTED | Spliterator.ORDERED |
Spliterator.DISTINCT | Spliterator.NONNULL;
}
@Override
public OfInt trySplit() {
return null;
}
@Override
public boolean tryAdvance(IntConsumer action) {
while (index < counts.length) {
final int count = counts[index++];
if (count != 0) {
action.accept(count);
return true;
}
}
return false;
}
}
Or with splitting allowed (because we can). The tryAdvance() is the same
just with a different end point:
static class IndexSpliterator implements Spliterator.OfInt {
int index;
final int end;
IndexSpliterator() {
this(0, counts.length);
}
IndexSpliterator(int start, int end) {
index = start;
this.end = end;
}
@Override
public long estimateSize() {
// This is an approximation.
// A Bloom filter that is at capacity will have approximately
// half of the bits set.
return (end - index) / 2;
}
@Override
public int characteristics() {
return Spliterator.SORTED | Spliterator.ORDERED |
Spliterator.DISTINCT | Spliterator.NONNULL;
}
@Override
public OfInt trySplit() {
final int middle = (index + end) >>> 1;
if (middle > index) {
final int start = index;
index = middle;
return new IndexSpliterator(start, middle);
}
return null;
}
@Override
public boolean tryAdvance(IntConsumer action) {
while (index < end) {
final int count = counts[index++];
if (count != 0) {
action.accept(count);
return true;
}
}
return false;
}
}
What do you think to changing the use of Iterator to Spliterator for
efficiency purposes?
This would add:
BloomFilter {
Spliterator.OfInt spliterator();
}
Hasher {
Spliterator.OfInt spliterator(Shape shape);
}
CountingBloomFilter extends BloomFilter {
// ???
Spliterator<int[]> countSpliterator();
}
The final one is for completeness so you can use the streams API with
the counts. I don't really like it. I'd prefer to pack the index and
count into a long as stated previously to maximise efficiency. My
suggestion would be to not have a spliterator for the counts and leave
the access of <index, count> pairs to an explicit forEach consumer.
Most of the current classes use a collection that provides a spliterator
so the change is easy. The DynamicHasher Iterator would have to be
rewritten but the Spliterator is simpler and all the code is already there.
I am not sold on adding a default stream method as is done in the
java.util.Collections API:
default IntStream stream() {
return StreamSupport.stream(spliterator(), false);
}
What do you think? I hope this is not going full circle back to an
earlier API which was previously discussed. My aim is to make the API as
efficient as possible and so starting with Spliterator rather than
Iterator seems to be a better approach.
On Mon, Mar 2, 2020 at 6:02 PM Alex Herbert <alex.d.herb...@gmail.com>
wrote:
On 02/03/2020 16:12, Claude Warren wrote:
Does getCounts() return a snapshot of the values when the call was made
or
does it return values that may be updated during the retrieval. If there
are 2 threads (one reading counts and one doing a merge) it seems to me
that the "iterate over the data without constructing objects" approach
means that the data may not be internally consistent. But then we don't
really check that issue in the other methods either. So let's go with
the
fail fast BitCountConsumer approach.
My assumption on this is that no filter is safe for concurrent use.
Allowing a merge while reading the state is a concurrency issue. I don't
think we want to go down the route of having fail-fast concurrency
checking using a 'modified count' strategy, i.e. all operations save the
current 'modified count' at the start and increment it at the end, if it
changes before the end then there has been concurrent modification. It
would be simpler to state that no filters are designed to be used
concurrently.
On the StaticHasher it is used for two purposes:
1) getting a list of enabled bits.
2) creating a bloom filter from a list of enabled bits. There was a
request early on for the ability to test membership in Bloom filter
without
having to construct a bloom filter. Basically, the developer has a list
of
values and wants to check membership.
I think the issue is that for 1 and 2 there are a few scenarios with
different requirements since the list of enabled bits can be small or big.
One feature of the StaticHasher is the requirement to remove duplicates
and return a sorted order. This allows for an efficient storage form
factor with the intension that it may be around for a while. But it is
an overhead when creating a large one from a known set of non-duplicate
bits, i.e. a Bloom filter.
For (2) if you want to do a dynamic check to test membership then you
use BloomFilter.contains(Hasher). I would pass an on-the-fly Hasher for
this and not construct the entire set of indices into a StaticHasher
anyway.
This would be done using the DynamicHasher to build hashes on-the-fly,
which may have duplicates. For the use case where you already know the
bit indices but do not want to create a BloomFilter or a StaticHasher
then perhaps we need another Hasher that is a wrapper around an int[]
that allows duplicates.
// Returns an unordered set of values that may contain duplicates.
static Hasher wrap(final int[] values, final Shape shape) {
Objects.requireNonNull(values);
Objects.requireNonNull(shape);
return new Hasher() {
@Override
public OfInt getBits(Shape sameShape) {
if (!shape.equals(sameShape)) {
throw new IllegalArgumentException();
}
return Arrays.stream(values).iterator();
}
@Override
public HashFunctionIdentity getHashFunctionIdentity() {
return shape.getHashFunctionIdentity();
}
@Override
public boolean isEmpty() {
return values.length == 0;
}
};
}
It might make more sense to reimplement the StaticHasher using a long[]
internally (like the BloomFilter.getBits() method returns). We have the
shape so we know the maximum length and we could trim it after loading to
remove trailing zero value longs. This would remove the necessity of
converting the iterator into a set of some sort. We can do the limit
checks quickly as we turn bits on.
For small numbers of indices the long[] format is likely to be less
space efficient.
Makes me think we might need to implement StandardBloomFilter to use
long[]
as well.
That is just the BitSetBloomFilter. So if you use this format in the
StaticHasher then you have no advantage over actually creating a
BitSetBloomFilter.
The StaticHasher is returned by the BloomFilter interface. You also have
a method to return the bits using the long[] format. So there is
redundancy here. To drop the redundancy I think you separate the uses
for the canonical representation of the entire filter as a long[] and
the uses for the set bits. If the later is satisfied by the StaticHasher
then it should be replaced by an iterator instead.
Looking at the code the getHasher() method in BloomFilter is only used
in HasherBloomFilter. This is to add more enabled bits to the current
set it contains. It seems that this use case is better served by using a
Set as the backing storage.
This leaves the StaticHasher with no usage in the current library. It is
not as fast as wrapping a provided array. It offers no expansion of
storage for use in the HasherBloomFilter. It does however provide the
smallest form for a compact BloomFilter representation. So it could be
renamed to ImmutableHasher.
I would think it best to consolidate all of this:
- StaticHasher to stay as an immutable instance of sorted bit indices.
The intention is an efficient compact form for a few bits of a
BloomFilter than can be merged efficiently. It could be used with
pre-exisiting indices but would have to eliminate duplicates and sort them.
- Remove the redundant StaticHasher constructor accepting a StaticHasher
instance since they are immutable.
- Possibly add a method to StaticHasher to merge another StaticHasher to
create a new instance.
- Possibly add a method to StaticHasher to get the maximum index in the
set (it already has size()). This helps convert it to a long[] or any
other class that will call getBits() and use the iterator output.
- BloomFilter to remove the getHasher() method. The long[] getBits()
method to be documented as returning the canonical format of the filter.
The getHasher() method is just duplicating this information in another
format.
- BloomFilter to have an iterator() method to get a
PrimitiveIterator.OfInt. This replaces the getHasher() method which just
provided access to the Shape and the PrimitiveIterator.OfInt of the
Hasher. BloomFilter already has getShape() so it just needs an iterator.
- HasherBloomFilter to use the iterator() method when merging a generic
BloomFilter. It can detect instances of HasherBloomFilter and switch to
a merge operation of its internal representation.
- HasherBloomFilter to use different backing storage (e.g. a
Set<Integer>) or adapt StaticHasher to be more efficient for merge.
- Add a new class akin to StaticHasher that allows duplicates. Document
it as a fast way to create a few bits of a BloomFilter.
You then have:
Hasher
- StaticHasher - immutable set of ordered non-duplicate bits. Can be
merged with another instance.
- DynamicHasher - generates bits on the fly using a hashing function
- FixedHasher - an array of indices. Can wrap an input array or be
created using constructors similar to StaticHasher but without the
guarantees of non-duplicates.
Lots to think about there.
Claude
On Mon, Mar 2, 2020 at 1:12 PM Alex Herbert <alex.d.herb...@gmail.com>
wrote:
On 02/03/2020 11:32, Claude Warren wrote:
my thought on changing the BloomFilter.merge() to return a boolean is
along
the lines you had: return true on successful merge (even if there are
no
changes in the enabled bits). And yes, for most cases the standard
bloom
filter will return true, but the change is really to support extensions
to
Bloom filter so I think it is reasonable.
As for the getCounts(). Suppose we split it into two methods:
// return the indexes that are enabled. This is equivalent to
CountingBloomFilter.getHasher().getBits( CountingBloomFilter.getShape()
);
Iterator<int> getIndexes()
// get the count for the specific index.
int getCount( int index );
With these methods It becomes possible to construct an iterator of
int[]
or
Map.Entry<Integer,Integer> or whatever else the developer wants.
Having to call getCount() for every index is likely to be slower than
all the garbage collection involved with iterating a disposable <index,
count> pair. For an array backed storage the access will be order(1).
But other storage may be a lot slower. This method ideally should
traverse the storage once and make each <index, count> pair available.
Ideally this would be without creating each <index, count> pair as a
disposable object.
Following on from previously, another disadvantage of the consumer
approach is the lack of fast fail. You can remedy this by adding a
boolean return from the consumer to indicate if you want to consume more
items:
interface BitCountConsumer {
boolean accept(int index, int count);
}
A CountingBloomFilter implementation then has something like:
void getCounts(BitCountConsumer consumer) {
while(hasNext()) {
next();
if (!consumer.accept(index(), count()) {
break;
}
}
}
Looking at the getHasher().getBits(...) idea I noticed that StaticHasher
is constructed using:
Iterator<Integer> iter
not:
PrimitiveIterator.OfInt
I'd prefer the primitive specialisation in this constructor. It would
break the HasherBloomFilter merge function but that can be fixed.
However it may be redundant. The StaticHasher has some oddities with the
available constructors:
public StaticHasher(final StaticHasher hasher, final Shape shape)
- why have a shape parameter? The constructor checks the shape is the
same as that for the hasher. So why not just a plain copy constructor:
public StaticHasher(final StaticHasher hasher)
This constructor is only used in the unit tests. Given the StaticHasher
is immutable then a copy constructor seems odd. I think it should be
dropped.
Here are is a constructor that is missing IMO:
public StaticHasher(final Set<Integer> indices, final Shape shape)
- Could be used to generically create a static hasher. The indices are
ensured to be unique by the Set but should be checked to be within the
shape.
With these constructors the public StaticHasher(final Iterator<Integer>
iter, final Shape shape) is only used by the BitSetBloomFilter:
public StaticHasher getHasher() {
return new StaticHasher(bitSet.stream().iterator(),
getShape());
}
Becomes:
public StaticHasher getHasher() {
return new
StaticHasher(bitSet.stream().boxed().collect(Collectors.toCollection(TreeSet::new)),
getShape());
}
This is a very roundabout way to construct a StaticHasher. Perhaps a
constructor accepting a BitSet would be useful?
So the API only requires:
public StaticHasher(final Hasher hasher, final Shape shape)
public StaticHasher(final Set<Integer> indices, final Shape shape)
// Maybe
public StaticHasher(final BitSet indices, final Shape shape)
I wondered about a merge function for the StaticHasher:
public StaticHasher merge(final StaticHasher other)
The merge function can make some assumptions about the two arrays to
merge as the class is final and the values are verified to be sorted and
within the Shape. However there is not a use for it other than in the
merge of two HasherBloomFilters, which is not a recommended operation
anyway.
Claude
On Mon, Mar 2, 2020 at 10:48 AM Alex Herbert <alex.d.herb...@gmail.com
wrote:
On 02/03/2020 09:38, Claude Warren wrote:
It is not too late to update the BloomFIlter interface to have the
merge
return a boolean. The incorrect Shape would still throw an
exception,
so
the return value would only come into play if the bits could not be
set.
thoughts?
I don't see the harm in it. But what would the return value be for?
For a standard collection it would be if the collection was changed by
the operation:
Collection.add/remove return "true if this collection changed as a
result of the call"
So here is the equivalent:
return "true if this filter was changed as a result of the call"
This is computationally slow to track. It also is confusing if the
filter was successfully merged but no bits were changed to then return
false because the filter was actually incorporated. So it would go
along
the lines that we discussed for the counting Bloom filter:
return "true if this filter was successfully merged as a result of the
call"
For most cases in the current library it would be true when an
exception
is not thrown. However the merge of the counting Bloom filter may have
reason to return false, e.g. overflow.
On Mon, Mar 2, 2020 at 7:56 AM Claude Warren <cla...@xenei.com>
wrote:
for the remove(), add(), and subtract() methods I agree that void is
not
correct and it should be boolean and be the same as the value you
would
get
from calling isValid().
You are correct the getCounts() should return an iterator of some
type
on
int[], I don't know why I thought long[]. I am happy with a plain
Iterator<int[]> as the return.
For the getCounts() method I am still looking for a way around having
to
create an <index, count> pair for everything in the filter. An
alternative to an iterator is to use the consumer idea. Given there is
no primitive specialisation of BiConsumer<T, U> in JDK 8 functions we
define our own:
interface BitCountConsumer {
void accept(int index, int count);
}
The CountingBloomFilter then has:
void forEachCount(BitCountConsumer consumer);
// Or
void getCounts(BitCountConsumer consumer);
You can then directly pass the counts from the backing storage to the
destination.
Advantages:
- No object creation
Disadvantages
- The counts cannot be streamed
An alternative is to provide an Iterator of long with the index and
count packed into a long with methods to extract them:
PrimativeIterator.OfLong getCounts();
default static int getIndex(long indexCountPair) {
return (int) (indexCountPair >>> 32);
}
default static int getCount(long indexCountPair) {
return (int) indexCountPair;
}
This will almost certainly be a cause for bugs/issues from users.
I believe that the counts will be used for 2 main use cases:
1. Storage
2. Adding to another counting Bloom filter
Both cases are likely to be done serially and not in parallel. So
providing a consumer based API to receive the counts would work.
WDYT?
Claude
On Mon, Mar 2, 2020 at 1:02 AM Alex Herbert <
alex.d.herb...@gmail.com
wrote:
On 1 Mar 2020, at 15:39, Claude Warren <cla...@xenei.com> wrote:
I think the CountingBloomFilter interface needs to extend
BloomFilter.
I said that but did not write it, sorry.
I think I am confused.
I would expect CountingBloomFilter to have
interface CountingBloomFilter extends BloomFilter {
// these 2 methods are the reverse of merge()
void remove( BloomFilter );
void remove( Hasher );
Fine. Same intention but different method names. But why void? It
forces
you to check if the remove was valid with a second call. On the
plus
side
it matches the void merge(…) methods and in most cases a user would
not
care to check anyway. If they are controlling the filter then leave
it
to
them to make sure they do not remove something they did not add.
// these 2 methods are the addition/subtraction of counts
void add( CountingBloomFilter )
void subtract( CountingBloomFilter );
Fine. But same comment as above with the void return.
// 2 methods to retrieve data
Stream<long[]> getCounts();
I don’t like this use of long[]. In my previous post I argued that
if
you
were to ever want to store more than max integer items in a filter
then the
Bloom filter would have more bit indices than max integer. So we
never
have
to support long counts. A filter that exceeds max integer for a
count
is
highly likely to be saturated and no use as a filter anyway.
For most backing implementations the object type of the stream will
be
different so you will have to write a Spliterator<T> implementation
or
wrap
some iterator anyway. So why not return the Spliterator:
Spliterator<int[]> getCounts();
Since the backing implementation will likely not store int[] pairs
then
this will have a lot of object creation and garbage collection
overhead to
go through the counts. This does not seem to be a big concern here
if
the
purpose is the same as for the BloomFilter for long[] getBits(),
i.e.
to
get a canonical representation for storage.
Note: The Spliterator may not have a known size (number of non zero
bits)
at creation, for example if the counts are stored in a fixed size
array.
Thus efficient parallel traversal by binary tree splitting is
limited
by
how evenly the counts are distributed. For a backing implementation
using a
collection then the size should be known. In this case a
Spliterator
would
be of more use than a plain Iterator. You can convert one to the
other
using:
java.util.Spliterators:
public static<T> Iterator<T> iterator(Spliterator<? extends T>
spliterator)
public static <T> Spliterator<T> spliterator(Iterator<? extends T>
iterator,
long size,
int
characteristics)
So which to choose for the API?
The Hasher currently uses an Iterator:
PrimitiveIterator.OfInt getBits(Shape shape);
In the case of a StaticHasher this could return a spliterator. But
the
DynamicHasher needs a reworking of the internal Iterator class. It
could be
a Spliterator to use the new IntConsumer API but in most (all)
cases
splitting would not be possible for dynamic hashing as the parts
are
produced in order. It is likely that they will be consumed
sequentially too.
I would suggest that Spliterator is the more modern implementation,
despite not always being applicable to parallelisation in a stream.
Currently the iterator from the Hasher is used in
forEachRemaining()
and
while loop is approximately equal measure. The while loops are for
a
fast
exit and would be uglier if rewritten for a
Spliterator.tryAdvance(IntConsumer) syntax.
There is a use of the IteratorChain in HasherBloomFilter that would
need
a rethink for spliterators.
The path of least resistance is to use Iterator<int[]> for the API
of
CountingBloomFilter to be consistent with Hasher’s use of Iterator.
WDYT?
boolean isValid()
Fine. Allows some level of feedback that the counts are corrupt.
}
Claude
On Sun, Mar 1, 2020 at 2:48 PM Alex Herbert <
alex.d.herb...@gmail.com
<mailto:alex.d.herb...@gmail.com>>
wrote:
On 1 Mar 2020, at 09:28, Claude Warren <cla...@xenei.com>
wrote:
The idea of a backing array is fine and the only problem I see
with
it is
in very large filters (on the order of 10^8 bits and larger) but
document
the size calculation and let the developer worry about it.
Let us look at the use case where we max out the array. Using the
Bloom
filter calculator:
n = 149,363,281
p = 0.001000025 (1 in 1000)
m = 2147483647 (256MiB)
k = 10
n = 74,681,641
p = 0.000001 (1 in 999950)
m = 2147483647 (256MiB)
k = 20
n = 49,787,761
p = 0.000000001 (1 in 999924899)
m = 2147483647 (256MiB)
k = 30
So you will be able to put somewhere in the order of 10^8 or 10^7
items
into the filter. I would say that anyone putting more than that
into
the
filter has an unusual use case. The CountingBloomFilter can throw
an
exception if m is too large and will throw an OutOfMemoryError if
you
cannot allocate an array large enough.
One clear point here is that you cannot use a short as a 16-bit
count
would easily overflow. So you have to use an integer array for
the
counts.
A maximum length int[] is roughly 8GB.
What would another implementation cost in terms of memory? The
TreeMap<Integer, Integer> was the most space efficient. In the
previous
e-mail the saturation of a Bloom filter bits was approximately
50%
when at
the intended capacity. So we have to estimate the size of a
TreeMap
containing Integer.MAX_VALUE/2 indices ~ 2^30. The memory test
shows
the
TreeMap memory scales linearly with entries:
32768 / 65536 (0.500) : TreeMap<Integer, Integer> =
1834061
bytes
65536 / 131072 (0.500) : TreeMap<Integer, Integer> =
3669080
bytes
131072 / 262144 (0.500) : TreeMap<Integer, Integer> =
7339090
bytes
So what is the memory for a TreeMap with 2^30 indices. I make it
about:
(2^30 / 131,072) * 7,339,090 bytes ~ 6e10 bytes = 55.99 GB
I would say that this amount of RAM is unusual. It is definitely
not
as
efficient as using an array. So very large counting Bloom filters
are
going
to require some thought as to the hardware they run on. This may
not
be the
case in 10 years time.
I would say that we try an int[] backing array for the storage
implementation and document it’s limitations. A different
implementation
could be provided in future if required.
This could be done by making CountingBloomFilter an interface
that
extends
BloomFilter with the methods:
subtract(BloomFilter filter)
subtract(Hasher filter)
These will negate the effect of the corresponding
merge(BloomFilter)
operation.
Do we also need access to the counts and add/subtract of another
CountingBloomFilter?:
add(CountingBloomFilter filter);
subtract(CountingBloomFilter filter);
Iterator<int[]> getCounts();
int getSize(); // Number of items added
The CountingBloomFilter is then an interface that defines how to
reverse
the merge of some bits into the filter.
My concern is the inefficiency of the creation of objects in any
method
that provides access to the counts (e.g. above using an iterator
as
for
Hasher.getBits()). I presume this method would be to allow some
type
of
storage/serialisation of the filter akin to the long[] getBits()
method of
BloomFilter. So it may be better done using a method:
int getCount(int index);
The caller can then use long[] getBits() to get the indices set
in
the
filter and then for each non-zero bit index call getCount(index).
Or
just
not include the method as the counts are only of concern when
storing
the
filter. This functionality is cleaner pushed into an
implementation.
In a previous post we discussed whether to throw an exception on
overflow/underflow or raise in an invalid flag. Using the invalid
flag
idea
the interface would be:
interface CountingBloomFilter {
int add(CountingBloomFilter filter);
int subtract(BloomFilter filter);
int subtract(Hasher filter);
int subtract(CountingBloomFilter filter);
int getStatus();
// Maybe
int getSize();
int getCount(int index);
}
The status would be negative if any operation
overflowed/underflowed,
or
zero if OK. The current status is returned by the add/subtract
methods.
However I note that overflow may not be a concern. The number of
items
to
add to a filter to create overflow would be using a filter with a
number of
bits that is unrealistic to store in memory:
n = 2147483647
p = 0.001000025 (1 in 1000)
m = 30875634182 (3.59GiB)
k = 10
If you want to add 2 billion items (and overflow an integer
count)
then
your filter would be so big it would break the rest of the API
that
uses a
32-bit int for the bit index.
Thus only underflow is a realistic concern. This could be
documented
as
handled in an implementation specific manner (i.e. throw or
ignore).
The
API is then simplified to:
interface CountingBloomFilter {
boolean add(CountingBloomFilter filter);
boolean subtract(BloomFilter filter);
boolean subtract(Hasher filter);
boolean subtract(CountingBloomFilter filter);
int getStatus();
// Maybe
int getSize();
int getCount(int index);
}
The boolean is used to state that add/subtract did not
over/underflow.
Implementations can throw if they require it.
The question then becomes what does getSize() represent if an
add/subtract
did not execute cleanly. Under this scheme it would be the number
of
(add -
subtract) operations. The status flag would be used to indicate
if
the
size
is valid, or any of the counts from getCount(). The simpler API
is
to
not
allow access to counts/size or adding/subtracting counts:
interface CountingBloomFilter {
boolean subtract(BloomFilter filter);
boolean subtract(Hasher filter);
int getStatus();
// Or something like ...
boolean isValid();
}
This filter is then only concerned with reversing the merge of
Bloom
filters with a valid status flag to indicate that the current
state
is
consistent (i.e. all filters have been cleanly
merged/subtracted).
WDYT?
As for the merge question. merge is a standard bloom filter
operation.
It
is well defined in the literature. Merging a bloom filter into
a
counting
bloom filter means incrementing the bit counts. I think that
merge/remove
should continue to operate as though the parameter were a
standard
bloom
filter.
OK. So the count is to represent the number of filters that had a
bit
set
at that index. This makes it more clear.
We had spoken of implementing and adding/deleting method pair
that
would
operate on CountingBloomFilters and would add/subtract the
counts.
(e.g.
add(CountingBloomFilter) and subtract(CountingBloomFilter))
I disagree with your proposal for the merge(Hasher)
implementation,
and I
am not certain that an add(Hasher) makes sense. First consider
that
the
Hasher returns the bits that are to be enabled in the Bloom
filter
so
collisions are expected. In the normal course of events a
Hasher
is
used
to create a normal Bloom filter where all the duplicates are
removed.
That
filter is then merged into a CountingBloomFilter. So in some
sense
the
Hasher and the normal Bloom filter are the same. So I would
expect
the
merge of the Hasher and the merge of the normal Bloom filter
created
from
that hasher into a CountingBloomFilter to yield the same result.
If
you
wanted to add an add(Hasher)/delete(Hasher) pair of functions
to a
CountingBloomFilter you could implement with duplicate counting,
but
I am
not certain of the validity of such a count and I fear that it
muddies
the
waters with respect to what the CountingBloomFilter is counting.
Agreed.
Claude
On Sat, Feb 29, 2020 at 2:13 PM Alex Herbert <
alex.d.herb...@gmail.com
<mailto:alex.d.herb...@gmail.com <mailto:
alex.d.herb...@gmail.com
wrote:
On 29 Feb 2020, at 07:46, Claude Warren <cla...@xenei.com
<mailto:
cla...@xenei.com> <mailto:
cla...@xenei.com <mailto:cla...@xenei.com>>> wrote:
Alex would you take a look at pull request 131 [1]. it adds a
new
hasher
implementation and makes the HashFunctionValidator available
for
public
use.
https://github.com/apache/commons-collections/pull/131 <
https://github.com/apache/commons-collections/pull/131> <
https://github.com/apache/commons-collections/pull/131 <
https://github.com/apache/commons-collections/pull/131>> <
https://github.com/apache/commons-collections/pull/131 <
https://github.com/apache/commons-collections/pull/131> <
https://github.com/apache/commons-collections/pull/131 <
https://github.com/apache/commons-collections/pull/131>>>
OK. I’ll take a look.
I’ve been thinking about the counting Bloom filter and the
backing
storage. In summary:
1. The backing storage should be a fixed array.
2. Merging a Hasher should count duplicate indices, not flatten
them
all
to a single count.
For background I’ve used the standard formulas to estimate the
number of
indices that will be non-zero in a Bloom filter. The wikipedia
page
gives
this formula for the expected number of bits set to 0 (E(q)) if
you
have
inserted i elements into a filter of size m using k hash
functions:
E(q) = (1 - 1/m)^ki"
So a rough guess of the number of indices (bits) used by a
filter
is
1-E(q).
Here is a table of Bloom filters with different collision
probabilities
and the proportion of bits that will be set when 1%, 10%, 100%
of
the
capacity of the filter has been met:
n p m k I E(q) bits
1000 1E-04 19171 13 10 0.9932 0.0068
1000 1E-04 19171 13 100 0.9344 0.0656
1000 1E-04 19171 13 1000 0.5076 0.4924
1000 1E-05 23963 17 10 0.9929 0.0071
1000 1E-05 23963 17 100 0.9315 0.0685
1000 1E-05 23963 17 1000 0.4919 0.5081
1000 1E-06 28756 20 10 0.9931 0.0069
1000 1E-06 28756 20 100 0.9328 0.0672
1000 1E-06 28756 20 1000 0.4988 0.5012
10000 1E-06 287552 20 100 0.9931 0.0069
10000 1E-06 287552 20 1000 0.9328 0.0672
10000 1E-06 287552 20 10000 0.4988 0.5012
The point is that if you create a Bloom filter and fill it to
10%
of
the
intended capacity the number of indices used will be about 6-7%
of
the
filter bits.
So how to store the counts? Currently the counting bloom filter
uses
a
TreeMap<Integer, Integer>. I tried:
TreeMap<Integer, Integer>
HashMap<Integer, Integer>
TreeSet<MutableCount>
HashSet<MutableCount>
int[]
The MutableCount is a custom object that stores the bit index
and
uses
it
for a hash code and then has a mutable integer count field. It
allows
the
count to be incremented/decremented if the object is in the
set:
static final class MutableCount implements
Comparable<MutableCount> {
final int key;
int count;
// etc
}
This is adapted from the Bag<T> collection which stores an item
count
with
a MutableInteger. Here the mutable count is part of the same
object T
inserted into the Set. So you can find the object, change the
count
and
not
have to put it back into the set. This is more efficient than
changing
the
Integer stored in a Map.
I’ve estimated memory usage using an idea based on this article
from
JavaWorld: Java Tip 130: Do you know your data size? [1].
Basically you:
- create an object and throw it away. All classes are then
initialised.
- Then you free memory (run garbage collection) and get the
current
memory
usage
- Then create a lot of your object (held in an array)
- Then measure memory usage again
- memory = (after - before) / count
Here is some example output for n bits set in size m:
13107 / 262144 (0.050) : TreeMap<Integer, Integer> =
733947
bytes
26214 / 262144 (0.100) : TreeMap<Integer, Integer> =
1467866
bytes
13107 / 262144 (0.050) : TreeSet<MutableCount> =
838928
bytes
26214 / 262144 (0.100) : TreeSet<MutableCount> =
1677776
bytes
13107 / 262144 (0.050) : HashMap<Integer, Integer> =
1677712
bytes
26214 / 262144 (0.100) : HashMap<Integer, Integer> =
2306739
bytes
13107 / 262144 (0.050) : HashSet<MutableCount> =
1782664
bytes
26214 / 262144 (0.100) : HashSet<MutableCount> =
2516656
bytes
0 / 262144 (0.000) : int[] =
1048608
bytes
0 / 262144 (0.000) : short[] =
524320
bytes
The estimate is accurate to 0.0001% for the arrays so the
method
is
working. The HashMap was created with the capacity set to the
expected
capacity of the filter (m).
I’ve chosen these sizes because at 5% full a HashSet is less
memory
efficient than using a fixed size array, and at 10% the TreeSet
is
also
less efficient.
Note that the java.util.Tree/HashSet versions just wrap a Map
and
insert a
dummy object for all keys in the Map. So here a Set is not as
efficient
as
a Map because in the Map test I always inserted the same
Integer
object
representing 1. This would be the same as using a Set with an
Integer
key
but here the Set had to contain the MutableCount which has an
extra
int
field and is larger than an Integer.
These data lead me to think that a counting Bloom filter should
just
use a
fixed size backing array:
- If created using the same Shape as a standard Bloom filter it
uses
a
fixed size. This has high memory cost when the filter is empty
but
when
it
exceeds 10% of the intended capacity it is more efficient than
a
dynamic
backing storage.
- All operations will operate in order(n) time for an operation
with
another filter with n indices. Each individual index count in
the
filter
will have order(1) time for access/update. Performance will be
limited
by
the memory cache of the entire array.
The issue is that a counting Bloom filter with a very low
number
of
inserted items will be memory inefficient. But under what
circumstance
will
such a filter be used in a short-term lifecycle? If it is
simply
to
merge
into another filter then this can be done using a merge with a
Hasher.
If
counts are to be merged then perhaps we provide a method to
merge
counts
using the same data structure returned by the
CountingBloomFilter
getCounts() method, e.g. using a stream of <index,count> pairs:
Stream<int[]> getCounts();
void add(Stream<int[]> counts);
The issue here is the Shape and HashFunctionIdentity of the
origin
of
the
merge cannot be validated. So just leave it out and use the
merge
with a
Hasher.
Thus the next issue with the counting Bloom filter
implementation.
Currently when it merges with a Hasher it puts all the indices
into a
Set
and so will only increment the count by 1 for each index
identified
by
the
Hasher. This appears to miss the entire point of the counting
Bloom
filter.
If I hash an objects to generate k indices I would hope that I
do
get k
indices. But the hash may not be perfect and I may get [1, k]
indices
with
some duplications. This is part of the signature of that object
with
the
given hash. So surely a counting Bloom filter should
accommodate
this.
If
my Hasher generates the same index 20 times this should result
in
the
count
of that index incrementing by 20.
The result if that if an object is added direct to a counting
Bloom
filter
using a Hasher it will have a different result that if added
to a
standard
Bloom filter and then that filter added to the counting Bloom
filter.
Opinions on this?
Alex
[1]
http://www.javaworld.com/javaworld/javatips/jw-javatip130.html
<
http://www.javaworld.com/javaworld/javatips/jw-javatip130.html>
On Tue, Feb 25, 2020 at 12:35 AM Alex Herbert <
alex.d.herb...@gmail.com <mailto:alex.d.herb...@gmail.com>>
wrote:
I have created a PR that contains most of the changes
discussed
in
this
thread (see [1]).
Please review the changes and comment here or on GitHub.
I have left the CountingBloomFilter alone. I will reimplement
the
add/subtract functionality as discussed into another PR.
Alex
[1] https://github.com/apache/commons-collections/pull/133 <
https://github.com/apache/commons-collections/pull/133> <
https://github.com/apache/commons-collections/pull/133 <
https://github.com/apache/commons-collections/pull/133>>
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