Re: [HACKERS] [PERFORM] Releasing memory during External sorting?

2005-09-26 Thread Dann Corbit


 -Original Message-
 From: Ron Peacetree [mailto:[EMAIL PROTECTED]
 Sent: Saturday, September 24, 2005 3:31 AM
 To: Dann Corbit; pgsql-hackers@postgresql.org; pgsql-
 [EMAIL PROTECTED]
 Subject: RE: [HACKERS] [PERFORM] Releasing memory during External
sorting?
 
 From: Dann Corbit [EMAIL PROTECTED]
 Sent: Sep 23, 2005 5:38 PM
 Subject: RE: [HACKERS] [PERFORM] Releasing memory during External
sorting?
 
 _C Unleashed_ also explains how to use a callback function to perform
 arbitrary radix sorts (you simply need a method that returns the
 [bucketsize] most significant bits for a given data type, for the
length
 of the key).
 
 So you can sort fairly arbitrary data in linear time (of course if
the
 key is long then O(n*log(n)) will be better anyway.)
 
 But in any case, if we are talking about external sorting, then disk
 time will be so totally dominant that the choice of algorithm is
 practically irrelevant.
 
 Horsefeathers.  Jim Gray's sorting contest site:
 http://research.microsoft.com/barc/SortBenchmark/

 proves that the choice of algorithm can have a profound affect on
 performance.  

Picklesmoke.  I was referring to the algorithm used to perform the sort
stage, and not the algorithm used to perform the IO which has a dominant
effect on the overall sort time.  I thought that should be clear from
context.

After all, the amount of IO done is the most
 important of the things that you should be optimizing for in
 choosing an external sorting algorithm.

Replacement selection uses a terrible O(f(n)) algorithm.  The only
reason it is a customary choice for external sorting is because the runs
are twice as long.

Using a classical merge sequence, you have half as many reads and writes
using replacement selection as with other methods.  That saves ONE read
and ONE write pass, because of having half as many subfiles.

Suppose, for instance, that you have 64 subfiles.  Using any classical
merge algorithm, they will have to be read and merged in a first pass,
giving 32, then again giving 16 then again giving 8 then again giving 4,
then again giving two and one final pass to create one file.

So, if replacement selection were applied, there would be 6 read/write
passes instead of seven in this problem set.  After the creation of the
original subfiles, the algorithm I listed reads once and writes once and
is done.

So what about the argument for skipping around?  Well, first of all the
OS is going to cache the reads to a large degree.  And second of all, if
we read a single record with no buffering and wrote a single record for
each operation, then because we only have to read once, that is better
than skipping around 7 times for every read and write because of
physically reading and writing the files over and over.

But don't take my word for it.  Try it yourself.  It is laughably
trivial to implement it.
 
 Clearly, if we know or can assume the range of the data in question
 the theoretical minimum amount of IO is one pass through all of the
 data (otherwise, we are back in O(lg(n!)) land ).  Equally clearly,
for
 HD's that one pass should involve as few seeks as possible.
 
 In fact, such a principle can be applied to _all_ forms of IO:  HD,
 RAM, and CPU cache.  The absolute best that any sort can
 possibly do is to make one pass through the data and deduce the
 proper ordering of the data during that one pass.
 
 It's usually also important that our algorithm be Stable, preferably
 Wholly Stable.
 
 Let's call such a sort Optimal External Sort (OES).  Just how much
 faster would it be than current practice?
 
 The short answer is the difference between how long it currently
 takes to sort a file vs how long it would take to cat the contents
 of the same file to a RAM buffer (_without_ displaying it). IOW,
 there's SIGNIFICANT room for improvement over current
 standard practice in terms of sorting performance, particularly
 external sorting performance.
 
 Since sorting is a fundamental operation in many parts of a DBMS,
 this is a Big Deal.
 
 This discussion has gotten my creative juices flowing.  I'll post
 some Straw Man algorithm sketches after I've done some more
 thought.
 
 Ron
 
  -Original Message-
  From: Dann Corbit [EMAIL PROTECTED]
  Sent: Friday, September 23, 2005 2:21 PM
  Subject: Re: [HACKERS] [PERFORM] Releasing memory during ...
 
 For the subfiles, load the top element of each subfile into a
priority
 queue.  Extract the min element and write it to disk.  If the next
 value is the same, then the queue does not need to be adjusted.
 If the next value in the subfile changes, then adjust it.
 
 Then, when the lowest element in the priority queue changes, adjust
 the queue.
 
 Keep doing that until the queue is empty.
 
 You can create all the subfiles in one pass over the data.
 
 You can read all the subfiles, merge them, and write them out in a
 second pass (no matter how many of them there are).
 
 The Gotcha with Priority Queues is that their performance depends

Re: [HACKERS] [PERFORM] Releasing memory during External sorting?

2005-09-25 Thread Simon Riggs
On Fri, 2005-09-23 at 12:48 -0400, Ron Peacetree wrote:

  I have some indications from private tests that very high memory settings
 may actually hinder performance of the sorts, though I cannot explain that
 and wonder whether it is the performance tests themselves that have issues.
 
 Hmmm.  Are you talking about amounts so high that you are throwing the OS
 into paging and swapping thrash behavior?  If not, then the above is weird.

Thanks for your thoughts. I'll retest, on the assumption that there is a
benefit, but there's something wrong with my earlier tests.

Best Regards, Simon Riggs



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Re: [HACKERS] [PERFORM] Releasing memory during External sorting?

2005-09-24 Thread Ron Peacetree
From: Dann Corbit [EMAIL PROTECTED]
Sent: Sep 23, 2005 5:38 PM
Subject: RE: [HACKERS] [PERFORM] Releasing memory during External sorting?

_C Unleashed_ also explains how to use a callback function to perform
arbitrary radix sorts (you simply need a method that returns the
[bucketsize] most significant bits for a given data type, for the length
of the key).

So you can sort fairly arbitrary data in linear time (of course if the
key is long then O(n*log(n)) will be better anyway.)

But in any case, if we are talking about external sorting, then disk
time will be so totally dominant that the choice of algorithm is
practically irrelevant.

Horsefeathers.  Jim Gray's sorting contest site:
http://research.microsoft.com/barc/SortBenchmark/

proves that the choice of algorithm can have a profound affect on
performance.  After all, the amount of IO done is the most
important of the things that you should be optimizing for in
choosing an external sorting algorithm.

Clearly, if we know or can assume the range of the data in question
the theoretical minimum amount of IO is one pass through all of the
data (otherwise, we are back in O(lg(n!)) land ).  Equally clearly, for
HD's that one pass should involve as few seeks as possible.

In fact, such a principle can be applied to _all_ forms of IO:  HD,
RAM, and CPU cache.  The absolute best that any sort can
possibly do is to make one pass through the data and deduce the
proper ordering of the data during that one pass.

It's usually also important that our algorithm be Stable, preferably
Wholly Stable.

Let's call such a sort Optimal External Sort (OES).  Just how much
faster would it be than current practice?

The short answer is the difference between how long it currently
takes to sort a file vs how long it would take to cat the contents
of the same file to a RAM buffer (_without_ displaying it). IOW, 
there's SIGNIFICANT room for improvement over current
standard practice in terms of sorting performance, particularly
external sorting performance.

Since sorting is a fundamental operation in many parts of a DBMS,
this is a Big Deal.
   
This discussion has gotten my creative juices flowing.  I'll post
some Straw Man algorithm sketches after I've done some more
thought.

Ron

 -Original Message-
 From: Dann Corbit [EMAIL PROTECTED]
 Sent: Friday, September 23, 2005 2:21 PM
 Subject: Re: [HACKERS] [PERFORM] Releasing memory during ...
 
For the subfiles, load the top element of each subfile into a priority
queue.  Extract the min element and write it to disk.  If the next
value is the same, then the queue does not need to be adjusted.
If the next value in the subfile changes, then adjust it.
 
Then, when the lowest element in the priority queue changes, adjust
the queue.
 
Keep doing that until the queue is empty.
 
You can create all the subfiles in one pass over the data.
 
You can read all the subfiles, merge them, and write them out in a
second pass (no matter how many of them there are).
 
The Gotcha with Priority Queues is that their performance depends
entirely on implementation.  In naive implementations either Enqueue()
or Dequeue() takes O(n) time, which reduces sorting time to O(n^2).

The best implementations I know of need O(lglgn) time for those
operations, allowing sorting to be done in O(nlglgn) time.
Unfortunately, there's a lot of data manipulation going on in the 
process and two IO passes are required to sort any given file.
Priority Queues do not appear to be very IO friendly.

I know of no sorting performance benchmark contest winner based on
Priority Queues.


Replacement selection is not a good idea any more, since obvious
better ideas should take over.  Longer runs are of no value if you do not
have to do multiple merge passes.
 
Judging from the literature and the contest winners, Replacement
Selection is still a viable and important technique.  Besides Priority
Queues, what obvious better ideas have you heard of?


I have explained this general technique in the book C Unleashed,
chapter 13.
 
Sample code is available on the book's home page.

URL please?  

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Re: [HACKERS] [PERFORM] Releasing memory during External sorting?

2005-09-23 Thread Ron Peacetree
From: Tom Lane [EMAIL PROTECTED]
Sent: Sep 23, 2005 2:15 PM
Subject: Re: [PERFORM] Releasing memory during External sorting? 

Mark Lewis [EMAIL PROTECTED] writes:
 operations != passes.  If you were clever, you could probably write a
 modified bubble-sort algorithm that only made 2 passes.  A pass is a
 disk scan, operations are then performed (hopefully in memory) on what
 you read from the disk.  So there's no theoretical log N lower-bound on
 the number of disk passes.

Given infinite memory that might be true, but I don't think I believe it
for limited memory.  If you have room for K tuples in memory then it's
impossible to perform more than K*N useful comparisons per pass (ie, as
each tuple comes off the disk you can compare it to all the ones
currently in memory; anything more is certainly redundant work).  So if
K  logN it's clearly not gonna work.

Actually, it's far better than that.  I recall a paper I saw in one of the
algorithms journals 15+ years ago that proved that if you knew the range
of the data, regardless of what that range was, and had n^2 space, you
could sort n items in O(n) time.

Turns out that with very modest constraints on the range of the data and
substantially less extra space (about the same as you'd need for
Replacement Selection + External Merge Sort), you can _still_ sort in
O(n) time.


It's possible that you could design an algorithm that works in a fixed
number of passes if you are allowed to assume you can hold O(log N)
tuples in memory --- and in practice that would probably work fine,
if the constant factor implied by the O() isn't too big.  But it's not
really solving the general external-sort problem.

If you know nothing about the data to be sorted and must guard against
the worst possible edge cases, AKA the classic definition of the general
external sorting problem,  then one can't do better than some variant
of Replacement Selection + Unbalanced Multiway Merge.

OTOH, ITRW things are _not_ like that.  We know the range of the data
in our DB fields or we can safely assume it to be relatively constrained.
This allows us access to much better external sorting algorithms.

For example Postman Sort (the 2005 winner of the PennySort benchmark)
is basically an IO optimized version of an external Radix Sort.


Ron

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Re: [HACKERS] [PERFORM] Releasing memory during External sorting?

2005-09-23 Thread Ron Peacetree
From: Simon Riggs [EMAIL PROTECTED]
Sent: Sep 23, 2005 5:37 AM
Subject: [PERFORM] Releasing memory during External sorting?

I have concerns about whether we are overallocating memory for use in
external sorts. (All code relating to this is in tuplesort.c)

A decent external sorting algorithm, say a Merge Sort + Radix (or
Distribution Counting) hybrid with appropriate optimizations for small sub-
files, should become more effective / efficient the more RAM you give it. 


The external sort algorithm benefits from some memory but not much.

That's probably an artifact of the psql external sorting code and _not_
due to some fundamental external sorting issue.


Knuth says that the amount of memory required is very low, with a value
typically less than 1 kB.

Required means the external sort can operate on that little memory.  How
Much memory is required for optimal performance is another matter.


I/O overheads mean that there is benefit from having longer sequential
writes, so the optimum is much larger than that. I've not seen any data
that indicates that a setting higher than 16 MB adds any value at all to a 
large external sort.

It should.  A first pass upper bound would be the amount of RAM needed for
Replacement Selection to create a run (ie sort) of the whole file.  That should
be ~ the amount of RAM to hold 1/2 the file in a Replacement Selection pass.

At the simplest, for any file over 32MB the optimum should be more than 
16MB.


 I have some indications from private tests that very high memory settings
may actually hinder performance of the sorts, though I cannot explain that
and wonder whether it is the performance tests themselves that have issues.

Hmmm.  Are you talking about amounts so high that you are throwing the OS
into paging and swapping thrash behavior?  If not, then the above is weird.


Does anyone have any clear data that shows the value of large settings
of work_mem when the data to be sorted is much larger than memory? (I am
well aware of the value of setting work_mem higher for smaller sorts, so
any performance data needs to reflect only very large sorts). 

This is not PostgreSQL specific, but it does prove the point that the 
performance
of external sorts benefits greatly from large amounts of RAM being available:

http://research.microsoft.com/barc/SortBenchmark/

Looking at the particulars of the algorithms listed there should shed a lot of 
light
on what a good external sorting algorithm looks like:
1= HD IO matters the most.
 1a= Seeking behavior is the largest factor in poor performance.
2= No optimal external sorting algorithm should use more than 2 passes.
3= Optimal external sorting algorithms should use 1 pass if at all possible.
4= Use as much RAM as possible, and use it as efficiently as possible.
5= The amount of RAM needed to hide the latency of a HD subsytem goes up as
the _square_ of the difference between the bandwidth of the HD subsystem and
memory.
6= Be cache friendly.
7= For large numbers of records whose sorting key is substantially smaller than
the record itself, use a pointer + compressed key representation and write the 
data
to HD in sorted order (Replace HD seeks with RAM seeks.  Minimize RAM seeks).
8= Since your performance will be constrained by HD IO first and RAM IO second,
up to a point it is worth it to spend more CPU cycles to save on IO.

Given the large and growing gap between CPU IO, RAM IO, and HD IO, these issues
are becoming more important for _internal_ sorts as well.  


Feedback, please.

Best Regards, Simon Riggs

Hope this is useful,
Ron

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Re: [HACKERS] [PERFORM] Releasing memory during External sorting?

2005-09-23 Thread Ron Peacetree
Yep.  Also, bear in mind that the lg(n!)= ~ nlgn - n lower bound on
the number of comparisions:
a= says nothing about the amount of data movement used.
b= only holds for generic comparison based sorting algorithms.

As Knuth says (vol 3, p180), Distribution Counting sorts without
ever comparing elements to each other at all, and so does Radix
Sort.  Similar comments can be found in many algorithms texts.

Any time we know that the range of the data to be sorted is substantially
restricted compared to the number of items to be sorted, we can sort in
less than O(lg(n!)) time.  DB fields tend to take on few values and are
therefore substantially restricted.

Given the proper resources and algorithms, O(n) sorts are very plausible
when sorting DB records.

All of the fastest external sorts of the last decade or so take advantage of
this.  Check out that URL I posted.

Ron


-Original Message-
From: Mark Lewis [EMAIL PROTECTED]
Sent: Sep 23, 2005 1:43 PM
To: Tom Lane [EMAIL PROTECTED]
Subject: Re: [PERFORM] Releasing memory during External sorting?

operations != passes.  If you were clever, you could probably write a
modified bubble-sort algorithm that only made 2 passes.  A pass is a
disk scan, operations are then performed (hopefully in memory) on what
you read from the disk.  So there's no theoretical log N lower-bound on
the number of disk passes.

Not that I have anything else useful to add to this discussion, just a
tidbit I remembered from my CS classes back in college :)

-- Mark

On Fri, 2005-09-23 at 13:17 -0400, Tom Lane wrote:
 Ron Peacetree [EMAIL PROTECTED] writes:
  2= No optimal external sorting algorithm should use more than 2 passes.
  3= Optimal external sorting algorithms should use 1 pass if at all possible.
 
 A comparison-based sort must use at least N log N operations, so it
 would appear to me that if you haven't got approximately log N passes
 then your algorithm doesn't work.
 
   regards, tom lane

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Re: [HACKERS] [PERFORM] Releasing memory during External sorting?

2005-09-23 Thread Mark Lewis
operations != passes.  If you were clever, you could probably write a
modified bubble-sort algorithm that only made 2 passes.  A pass is a
disk scan, operations are then performed (hopefully in memory) on what
you read from the disk.  So there's no theoretical log N lower-bound on
the number of disk passes.

Not that I have anything else useful to add to this discussion, just a
tidbit I remembered from my CS classes back in college :)

-- Mark

On Fri, 2005-09-23 at 13:17 -0400, Tom Lane wrote:
 Ron Peacetree [EMAIL PROTECTED] writes:
  2= No optimal external sorting algorithm should use more than 2 passes.
  3= Optimal external sorting algorithms should use 1 pass if at all possible.
 
 A comparison-based sort must use at least N log N operations, so it
 would appear to me that if you haven't got approximately log N passes
 then your algorithm doesn't work.
 
   regards, tom lane
 
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Re: [HACKERS] [PERFORM] Releasing memory during External sorting?

2005-09-23 Thread Dann Corbit
For the subfiles, load the top element of each subfile into a priority
queue.  Extract the min element and write it to disk.  If the next value
is the same, then the queue does not need to be adjusted.  If the next
value in the subfile changes, then adjust it.

Then, when the lowest element in the priority queue changes, adjust the
queue.

Keep doing that until the queue is empty.

You can create all the subfiles in one pass over the data.

You can read all the subfiles, merge them, and write them out in a
second pass (no matter how many of them there are).

Replacement selection is not a good idea any more, since obvious better
ideas should take over.  Longer runs are of no value if you do not have
to do multiple merge passes.

I have explained this general technique in the book C Unleashed,
chapter 13.

Sample code is available on the book's home page.

 -Original Message-
 From: [EMAIL PROTECTED] [mailto:pgsql-hackers-
 [EMAIL PROTECTED] On Behalf Of Ron Peacetree
 Sent: Friday, September 23, 2005 11:41 AM
 To: Mark Lewis; Tom Lane; pgsql-hackers@postgresql.org; pgsql-
 [EMAIL PROTECTED]
 Subject: Re: [HACKERS] [PERFORM] Releasing memory during External
sorting?
 
 Yep.  Also, bear in mind that the lg(n!)= ~ nlgn - n lower bound on
 the number of comparisions:
 a= says nothing about the amount of data movement used.
 b= only holds for generic comparison based sorting algorithms.
 
 As Knuth says (vol 3, p180), Distribution Counting sorts without
 ever comparing elements to each other at all, and so does Radix
 Sort.  Similar comments can be found in many algorithms texts.
 
 Any time we know that the range of the data to be sorted is
substantially
 restricted compared to the number of items to be sorted, we can sort
in
 less than O(lg(n!)) time.  DB fields tend to take on few values and
are
 therefore substantially restricted.
 
 Given the proper resources and algorithms, O(n) sorts are very
plausible
 when sorting DB records.
 
 All of the fastest external sorts of the last decade or so take
advantage
 of
 this.  Check out that URL I posted.
 
 Ron
 
 
 -Original Message-
 From: Mark Lewis [EMAIL PROTECTED]
 Sent: Sep 23, 2005 1:43 PM
 To: Tom Lane [EMAIL PROTECTED]
 Subject: Re: [PERFORM] Releasing memory during External sorting?
 
 operations != passes.  If you were clever, you could probably write a
 modified bubble-sort algorithm that only made 2 passes.  A pass is a
 disk scan, operations are then performed (hopefully in memory) on what
 you read from the disk.  So there's no theoretical log N lower-bound
on
 the number of disk passes.
 
 Not that I have anything else useful to add to this discussion, just a
 tidbit I remembered from my CS classes back in college :)
 
 -- Mark
 
 On Fri, 2005-09-23 at 13:17 -0400, Tom Lane wrote:
  Ron Peacetree [EMAIL PROTECTED] writes:
   2= No optimal external sorting algorithm should use more than 2
 passes.
   3= Optimal external sorting algorithms should use 1 pass if at all
 possible.
 
  A comparison-based sort must use at least N log N operations, so it
  would appear to me that if you haven't got approximately log N
passes
  then your algorithm doesn't work.
 
  regards, tom lane
 
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Re: [HACKERS] [PERFORM] Releasing memory during External sorting?

2005-09-23 Thread Tom Lane
Ron Peacetree [EMAIL PROTECTED] writes:
 2= No optimal external sorting algorithm should use more than 2 passes.
 3= Optimal external sorting algorithms should use 1 pass if at all possible.

A comparison-based sort must use at least N log N operations, so it
would appear to me that if you haven't got approximately log N passes
then your algorithm doesn't work.

regards, tom lane

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Re: [HACKERS] [PERFORM] Releasing memory during External sorting?

2005-09-23 Thread Tom Lane
Mark Lewis [EMAIL PROTECTED] writes:
 operations != passes.  If you were clever, you could probably write a
 modified bubble-sort algorithm that only made 2 passes.  A pass is a
 disk scan, operations are then performed (hopefully in memory) on what
 you read from the disk.  So there's no theoretical log N lower-bound on
 the number of disk passes.

Given infinite memory that might be true, but I don't think I believe it
for limited memory.  If you have room for K tuples in memory then it's
impossible to perform more than K*N useful comparisons per pass (ie, as
each tuple comes off the disk you can compare it to all the ones
currently in memory; anything more is certainly redundant work).  So if
K  logN it's clearly not gonna work.

It's possible that you could design an algorithm that works in a fixed
number of passes if you are allowed to assume you can hold O(log N)
tuples in memory --- and in practice that would probably work fine,
if the constant factor implied by the O() isn't too big.  But it's not
really solving the general external-sort problem.

regards, tom lane

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Re: [HACKERS] [PERFORM] Releasing memory during External sorting?

2005-09-23 Thread Dann Corbit
The cited book also explains how to use a callback function to perform
arbitrary radix sorts (you simply need a method that returns the
[bucketsize] most significant bits for a given data type, for the length
of the key).

So you can sort fairly arbitrary data in linear time (of course if the
key is long then O(n*log(n)) will be better anyway.)

But in any case, if we are talking about external sorting, then disk
time will be so totally dominant that the choice of algorithm is
practically irrelevant.

 -Original Message-
 From: [EMAIL PROTECTED] [mailto:pgsql-hackers-
 [EMAIL PROTECTED] On Behalf Of Dann Corbit
 Sent: Friday, September 23, 2005 2:21 PM
 To: Ron Peacetree; Mark Lewis; Tom Lane; pgsql-hackers@postgresql.org;
 pgsql-performance@postgresql.org
 Subject: Re: [HACKERS] [PERFORM] Releasing memory during External
sorting?
 
 For the subfiles, load the top element of each subfile into a priority
 queue.  Extract the min element and write it to disk.  If the next
value
 is the same, then the queue does not need to be adjusted.  If the next
 value in the subfile changes, then adjust it.
 
 Then, when the lowest element in the priority queue changes, adjust
the
 queue.
 
 Keep doing that until the queue is empty.
 
 You can create all the subfiles in one pass over the data.
 
 You can read all the subfiles, merge them, and write them out in a
 second pass (no matter how many of them there are).
 
 Replacement selection is not a good idea any more, since obvious
better
 ideas should take over.  Longer runs are of no value if you do not
have
 to do multiple merge passes.
 
 I have explained this general technique in the book C Unleashed,
 chapter 13.
 
 Sample code is available on the book's home page.
 
  -Original Message-
  From: [EMAIL PROTECTED] [mailto:pgsql-hackers-
  [EMAIL PROTECTED] On Behalf Of Ron Peacetree
  Sent: Friday, September 23, 2005 11:41 AM
  To: Mark Lewis; Tom Lane; pgsql-hackers@postgresql.org; pgsql-
  [EMAIL PROTECTED]
  Subject: Re: [HACKERS] [PERFORM] Releasing memory during External
 sorting?
 
  Yep.  Also, bear in mind that the lg(n!)= ~ nlgn - n lower bound on
  the number of comparisions:
  a= says nothing about the amount of data movement used.
  b= only holds for generic comparison based sorting algorithms.
 
  As Knuth says (vol 3, p180), Distribution Counting sorts without
  ever comparing elements to each other at all, and so does Radix
  Sort.  Similar comments can be found in many algorithms texts.
 
  Any time we know that the range of the data to be sorted is
 substantially
  restricted compared to the number of items to be sorted, we can sort
 in
  less than O(lg(n!)) time.  DB fields tend to take on few values and
 are
  therefore substantially restricted.
 
  Given the proper resources and algorithms, O(n) sorts are very
 plausible
  when sorting DB records.
 
  All of the fastest external sorts of the last decade or so take
 advantage
  of
  this.  Check out that URL I posted.
 
  Ron
 
 
  -Original Message-
  From: Mark Lewis [EMAIL PROTECTED]
  Sent: Sep 23, 2005 1:43 PM
  To: Tom Lane [EMAIL PROTECTED]
  Subject: Re: [PERFORM] Releasing memory during External sorting?
 
  operations != passes.  If you were clever, you could probably write
a
  modified bubble-sort algorithm that only made 2 passes.  A pass is a
  disk scan, operations are then performed (hopefully in memory) on
what
  you read from the disk.  So there's no theoretical log N lower-bound
 on
  the number of disk passes.
 
  Not that I have anything else useful to add to this discussion, just
a
  tidbit I remembered from my CS classes back in college :)
 
  -- Mark
 
  On Fri, 2005-09-23 at 13:17 -0400, Tom Lane wrote:
   Ron Peacetree [EMAIL PROTECTED] writes:
2= No optimal external sorting algorithm should use more than 2
  passes.
3= Optimal external sorting algorithms should use 1 pass if at
all
  possible.
  
   A comparison-based sort must use at least N log N operations, so
it
   would appear to me that if you haven't got approximately log N
 passes
   then your algorithm doesn't work.
  
 regards, tom lane
 
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