Re: Balanced trees

From	Roy Smith <roy@panix.com>
Newsgroups	comp.lang.python
Subject	Re: Balanced trees
Date	2014-03-19 10:06 -0400
Organization	PANIX Public Access Internet and UNIX, NYC
Message-ID	<roy-0F0BB4.10062919032014@news.panix.com> (permalink)
References	(15 earlier) <mailman.8264.1395181297.18130.python-list@python.org> <87r45zf6fu.fsf@elektro.pacujo.net> <5328efab$0$29994$c3e8da3$5496439d@news.astraweb.com> <87pplipo82.fsf@elektro.pacujo.net> <53299eac$0$29994$c3e8da3$5496439d@news.astraweb.com>

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In article <53299eac$0$29994$c3e8da3$5496439d@news.astraweb.com>,
 Steven D'Aprano <steve+comp.lang.python@pearwood.info> wrote:

> If you have a million items, then the odds that those 
> million items happen to be sorted (the worst-case order) are 1 in a 
> million factorial. That's a rather small number, small enough that we can 
> discount it from ever happening, not in a million lifetimes of the 
> Universe.

If the items are coming from some inherently random process, then I 
agree.  But, not all data sources are random.

Imagine you had a web site, and wanted to store various bits of data 
from the stream of input requests.  You decided that the data structure 
you were going to use was a balanced tree.  If your keys were, say, a 
hash of the client's IP address, then it's a pretty good guess they're 
random.  But, what if the keys were the time the request was received?  
Those are obviously not random, and using them as a keys in a balanced 
tree would give you sub-optimum performance.

This is not a hypothetical scenario.  Songza uses MongoDB as our 
database.  The indexes are balanced trees.  One of our biggest 
collections has a multi-component key, one of the components being the 
request time truncated to the hour.  Insertion time into that collection 
has an obvious sawtooth shape, with performance degrading as each hour 
progresses and jumping back up as the time rolls over to the next hour.  
This is due (we believe :-)) to the constant rebalancing of the index 
trees.

Almost-sorted data sets are very common.  For example, here's a pipeline 
I run a lot (from memory, could have gotten some detail wrong):

grep pattern lofgile | awk '{print $7}' | sed 's/:[0-9][0-9]$//' | sort 
| uniq -c

Field 7 is the timestamp for when a request came in.  What I'm doing 
here is counting how many requests of a certain type came in during each 
minute of the day.  Logging isn't exactly in chronological order, so I 
need to sort the times before I count them.  But, it's in *almost* 
chronological order; a sort which had pathologically bad behavior on 
almost sorted data would be unusable here.

Thread

Re: Tuples and immutability Duncan Booth <duncan.booth@invalid.invalid> - 2014-03-07 09:33 +0000
  Re: Tuples and immutability Ben Finney <ben+python@benfinney.id.au> - 2014-03-07 22:04 +1100
  Re: Tuples and immutability Chris Angelico <rosuav@gmail.com> - 2014-03-07 22:11 +1100
  Re: Tuples and immutability Peter Otten <__peter__@web.de> - 2014-03-07 12:38 +0100
  Re: Tuples and immutability Chris Angelico <rosuav@gmail.com> - 2014-03-07 22:45 +1100
  Re: Tuples and immutability Alister <alister.ware@ntlworld.com> - 2014-03-07 11:51 +0000
    Re: Tuples and immutability Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-07 11:23 -0700
  Re: Tuples and immutability Roy Smith <roy@panix.com> - 2014-03-07 08:37 -0500
  Re: Tuples and immutability Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-03-08 15:17 +1300
    Re: Tuples and immutability Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-07 21:17 -0700
      Balanced trees (was: Re: Tuples and immutability) Marko Rauhamaa <marko@pacujo.net> - 2014-03-08 10:34 +0200
        Re: Balanced trees (was: Re: Tuples and immutability) Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-08 04:03 -0700
          Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-08 13:26 +0200
        Re: Balanced trees (was: Re: Tuples and immutability) Dan Stromberg <drsalists@gmail.com> - 2014-03-08 11:58 -0800
        Re: Balanced trees Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-03-08 20:37 +0000
          Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-08 23:21 +0200
            Re: Balanced trees Roy Smith <roy@panix.com> - 2014-03-08 17:22 -0500
              Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-09 11:17 +0200
            Re: Balanced trees Dan Stromberg <drsalists@gmail.com> - 2014-03-08 17:31 -0800
              Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-09 11:27 +0200
                Re: Balanced trees Dan Stromberg <drsalists@gmail.com> - 2014-03-09 14:20 -0700
                Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-09 23:32 +0200
                Re: Balanced trees Dan Stromberg <drsalists@gmail.com> - 2014-03-09 14:37 -0700
                Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-09 23:43 +0200
                Re: Balanced trees Dan Stromberg <drsalists@gmail.com> - 2014-03-09 15:08 -0700
                Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-10 00:24 +0200
                Re: Balanced trees Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-09 18:04 -0600
                Re: Balanced trees Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-10 03:24 +0000
                Re: Balanced trees Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-10 03:24 +0000
                Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-10 08:16 +0200
                Re: Balanced trees Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-10 08:53 +0000
                Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-10 11:41 +0200
                Re: Balanced trees Ned Batchelder <ned@nedbatchelder.com> - 2014-03-10 06:57 -0400
                Re: Balanced trees Rustom Mody <rustompmody@gmail.com> - 2014-03-10 09:01 -0700
                Re: Balanced trees Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-11 02:02 +0000
                Re: Balanced trees Roy Smith <roy@panix.com> - 2014-03-10 22:20 -0400
                Re: Balanced trees Chris Angelico <rosuav@gmail.com> - 2014-03-11 13:29 +1100
                Re: Balanced trees Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-03-10 09:51 +0000
                Re: Balanced trees Roy Smith <roy@panix.com> - 2014-03-10 09:59 -0400
                Re: Balanced trees Chris Angelico <rosuav@gmail.com> - 2014-03-11 03:20 +1100
                Re: Balanced trees Chris Angelico <rosuav@gmail.com> - 2014-03-11 03:24 +1100
                Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-10 19:08 +0200
                Re: Balanced trees Chris Angelico <rosuav@gmail.com> - 2014-03-11 04:17 +1100
                Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-10 19:34 +0200
                Re: Balanced trees Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-13 12:40 -0600
                Re: Balanced trees Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-13 23:57 +0000
                Re: Balanced trees Dan Stromberg <drsalists@gmail.com> - 2014-03-13 20:12 -0700
                Re: Balanced trees Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-14 05:02 +0000
                Re: Balanced trees Roy Smith <roy@panix.com> - 2014-03-10 19:24 -0400
                Re: Balanced trees Chris Angelico <rosuav@gmail.com> - 2014-03-11 10:27 +1100
                Re: Balanced trees Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-11 01:26 +0000
                Re: Balanced trees Chris Angelico <rosuav@gmail.com> - 2014-03-11 12:45 +1100
                Re: Balanced trees Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-10 21:38 -0600
                Re: Balanced trees Chris Angelico <rosuav@gmail.com> - 2014-03-11 15:28 +1100
                Re: Balanced trees "Rhodri James" <rhodri@wildebst.org.uk> - 2014-03-12 00:57 +0000
                Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-11 12:12 +0200
                Re: Balanced trees alex23 <wuwei23@gmail.com> - 2014-03-12 10:13 +1000
                Re: Balanced trees Alister <alister.ware@ntlworld.com> - 2014-03-11 09:25 +0000
                Re: Balanced trees Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2014-03-12 10:08 +0100
                Re: Balanced trees Tim Chase <python.list@tim.thechases.com> - 2014-03-10 11:33 -0500
                Re: Balanced trees Chris Angelico <rosuav@gmail.com> - 2014-03-11 03:39 +1100
                Re: Balanced trees Dan Stromberg <drsalists@gmail.com> - 2014-03-10 18:05 -0700
                Re: Balanced trees Roy Smith <roy@panix.com> - 2014-03-10 22:13 -0400
                Re: Balanced trees Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2014-03-10 19:57 -0400
        Re: Balanced trees Joshua Landau <joshua@landau.ws> - 2014-03-15 01:13 +0000
          Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-18 00:05 +0200
            Re: Balanced trees Dan Stromberg <drsalists@gmail.com> - 2014-03-18 12:26 -0700
              Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-18 22:55 +0200
                Re: Balanced trees Dan Stromberg <drsalists@gmail.com> - 2014-03-18 14:45 -0700
                Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-19 00:03 +0200
                Re: Balanced trees Dan Stromberg <drsalists@gmail.com> - 2014-03-18 15:21 -0700
                Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-19 01:11 +0200
                Re: Balanced trees Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-19 01:15 +0000
                Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-19 10:49 +0200
                Re: Balanced trees Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-19 13:42 +0000
                Re: Balanced trees Marko Rauhamaa <marko@pacujo.net> - 2014-03-19 15:54 +0200
                Re: Balanced trees Roy Smith <roy@panix.com> - 2014-03-19 10:06 -0400
                Re: Balanced trees Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-19 01:15 +0000
                Re: Balanced trees Ethan Furman <ethan@stoneleaf.us> - 2014-03-19 08:15 -0700
                Re: Balanced trees "Rhodri James" <rhodri@wildebst.org.uk> - 2014-03-20 02:16 +0000
                Re: Balanced trees Dan Stromberg <drsalists@gmail.com> - 2014-03-19 19:34 -0700
                Re: Balanced trees Chris Kaynor <ckaynor@zindagigames.com> - 2014-03-18 18:02 -0700
            Re: Balanced trees Daniel Stutzbach <stutzbach@google.com> - 2014-03-18 13:18 -0700
        blist in standard library  (was Re: Balanced trees) Mark Lawrence <breamoreboy@yahoo.co.uk> - 2014-03-15 12:31 +0000
        Re: Balanced trees Daniel Stutzbach <stutzbach@google.com> - 2014-03-17 14:16 -0700
        Re: Balanced trees Joshua Landau <joshua@landau.ws> - 2014-03-18 00:08 +0000
        Re: Balanced trees Daniel Stutzbach <stutzbach@google.com> - 2014-03-17 18:01 -0700
        Re: Balanced trees Joshua Landau <joshua@landau.ws> - 2014-03-18 07:46 +0000
      Re: Tuples and immutability Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-03-09 13:40 +1300
        Re: Tuples and immutability Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-08 19:39 -0700
          Re: Tuples and immutability Marko Rauhamaa <marko@pacujo.net> - 2014-03-09 11:35 +0200
          Re: Tuples and immutability Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-03-10 11:03 +1300
            Re: Tuples and immutability Terry Reedy <tjreedy@udel.edu> - 2014-03-09 19:00 -0400
            Re: Tuples and immutability Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-09 17:42 -0600
              Re: Tuples and immutability Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-10 02:37 +0000
                Re: Tuples and immutability Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-10 02:35 -0600
                Re: Tuples and immutability Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-10 09:13 +0000
                Re: Tuples and immutability Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-03-11 18:15 +1300
              Re: Tuples and immutability Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-03-11 18:03 +1300
                Re: Tuples and immutability Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-11 04:39 -0600
                Re: Tuples and immutability Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-11 16:46 +0000
                Re: Tuples and immutability Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-03-12 10:23 +1300
                Re: Tuples and immutability Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-11 17:06 -0600
                Re: Tuples and immutability Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2014-03-12 23:20 +0000
                Re: Tuples and immutability Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-12 19:35 -0600
                Re: Tuples and immutability Terry Reedy <tjreedy@udel.edu> - 2014-03-12 22:09 -0400
      Re: Tuples and immutability Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2014-03-09 13:45 +1300
        Re: Tuples and immutability Ian Kelly <ian.g.kelly@gmail.com> - 2014-03-08 19:55 -0700

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