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Re: Algorithm that makes maximum compression of completly diffused data.

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From Joshua Landau <joshua@landau.ws>
Date 2013-11-03 15:34 +0000
Subject Re: Algorithm that makes maximum compression of completly diffused data.
Newsgroups comp.lang.python
Message-ID <mailman.1986.1383492895.18130.python-list@python.org> (permalink)

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On 3 November 2013 03:17, Steven D'Aprano
<steve+comp.lang.python@pearwood.info> wrote:
> On Sat, 02 Nov 2013 14:31:09 -0700, Tim Roberts wrote:
>
>> jonas.thornvall@gmail.com wrote:
>>>
>>>Well then i have news for you.
>>
>> Well, then, why don't you share it?
>>
>> Let me try to get you to understand WHY what you say is impossible.
> [snip reasons]
>
> But your second reason, better known as the pigeonhole principle,
> demonstrates that for any lossless compression method, there must be data
> sets that actually expand the data. It doesn't matter how cleverly you
> compress the data, you can't fit 20kg of potatoes in a 10kg bag, so to
> speak. Suppose your compression algorithm compresses a single byte into a
> nybble (four bits). There are 256 different input data sets (0x00,
> 0x01, ... 0xFF) and only 16 different outputs (0x0, 0x1, ... 0xF). There
> is no way for 256 pigeons to fit in 16 pigeon holes unless you put two or
> more pigeons in at least one hole. Ergo, if the compression algorithm is
> lossless, *some* data must be expanded rather than compressed.

You have to be careful to make this totally rigorous, too.

Note that I *can* make a "compression" algorithm that takes any
length-n sequence and compresses all but one sequence by at least one
bit, and does not ever expand the data.

"00" -> ""
"01" -> "0"
"10" -> "1"
"11" -> "00"

This, obviously, is just 'cause the length is an extra piece of data,
but sometimes you have to store that anyway ;). So if I have a list of
N length-Y lists containing only 1s or 0s, I can genuinely compress
the whole structure by N log2 Y items.

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Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-10-30 11:21 -0700
  Re: Algorithm that makes maximum compression of completly diffused data. Mark Lawrence <breamoreboy@yahoo.co.uk> - 2013-10-30 18:53 +0000
    Re: Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-10-30 12:01 -0700
      Re: Algorithm that makes maximum compression of completly diffused data. Mark Lawrence <breamoreboy@yahoo.co.uk> - 2013-10-30 19:18 +0000
        Re: Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-10-30 12:22 -0700
          Re: Algorithm that makes maximum compression of completly diffused data. Mark Lawrence <breamoreboy@yahoo.co.uk> - 2013-10-30 19:31 +0000
        Re: Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-10-30 12:23 -0700
          Re: Algorithm that makes maximum compression of completly diffused data. Mark Lawrence <breamoreboy@yahoo.co.uk> - 2013-10-30 19:35 +0000
          Re: Algorithm that makes maximum compression of completly diffused data. Ethan Furman <ethan@stoneleaf.us> - 2013-11-02 21:26 -0700
      Re: Algorithm that makes maximum compression of completly diffused data. Antoon Pardon <antoon.pardon@rece.vub.ac.be> - 2013-10-30 20:28 +0100
      Re: Algorithm that makes maximum compression of completly diffused data. Joshua Landau <joshua@landau.ws> - 2013-10-30 21:30 +0000
        Re: Algorithm that makes maximum compression of completly diffused data. rusi <rustompmody@gmail.com> - 2013-10-31 05:54 -0700
      Re: Algorithm that makes maximum compression of completly diffused data. Mark Lawrence <breamoreboy@yahoo.co.uk> - 2013-10-30 21:52 +0000
      Re: Algorithm that makes maximum compression of completly diffused data. Tim Chase <python.list@tim.thechases.com> - 2013-10-30 18:01 -0500
      Re: Algorithm that makes maximum compression of completly diffused data. Chris Angelico <rosuav@gmail.com> - 2013-10-31 10:41 +1100
  Re: Algorithm that makes maximum compression of completly diffused data. Dan Stromberg <drsalists@gmail.com> - 2013-10-30 12:29 -0700
  Re: Algorithm that makes maximum compression of completly diffused data. Tim Delaney <timothy.c.delaney@gmail.com> - 2013-10-31 06:35 +1100
    Re: Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-10-30 12:47 -0700
  Re: Algorithm that makes maximum compression of completly diffused data. Modulok <modulok@gmail.com> - 2013-10-30 13:46 -0600
    Re: Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-10-30 12:47 -0700
      Re: Algorithm that makes maximum compression of completly diffused data. Gene Heskett <gheskett@wdtv.com> - 2013-10-30 16:32 -0400
      Re: Algorithm that makes maximum compression of completly diffused data. Tim Roberts <timr@probo.com> - 2013-11-02 14:31 -0700
        Re: Algorithm that makes maximum compression of completly diffused data. Mark Janssen <dreamingforward@gmail.com> - 2013-11-02 14:37 -0700
        Re: Algorithm that makes maximum compression of completly diffused data. Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-11-03 03:17 +0000
          Re: Algorithm that makes maximum compression of completly diffused data. Chris Angelico <rosuav@gmail.com> - 2013-11-03 15:10 +1100
          Re: Algorithm that makes maximum compression of completly diffused data. Joshua Landau <joshua@landau.ws> - 2013-11-03 15:34 +0000
          Re: Algorithm that makes maximum compression of completly diffused data. Joshua Landau <joshua@landau.ws> - 2013-11-03 15:51 +0000
          Re: Algorithm that makes maximum compression of completly diffused data. Mark Janssen <dreamingforward@gmail.com> - 2013-11-03 19:40 -0800
          Re: Algorithm that makes maximum compression of completly diffused data. Tim Chase <python.list@tim.thechases.com> - 2013-11-04 07:08 -0600
        Re: Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-11-04 05:53 -0800
          Re: Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-11-04 06:00 -0800
          Re: Algorithm that makes maximum compression of completly diffused
 data. Dave Angel <davea@davea.name> - 2013-11-04 08:27 -0600
            Re: Algorithm that makes maximum compression of completly diffused data. rusi <rustompmody@gmail.com> - 2013-11-04 06:46 -0800
            Re: Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-11-04 14:34 -0800
              Re: Algorithm that makes maximum compression of completly diffused
 data. Dave Angel <davea@davea.name> - 2013-11-04 19:29 -0600
              Re: Algorithm that makes maximum compression of completly diffused data. Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-11-05 04:33 +0000
                Re: Algorithm that makes maximum compression of completly diffused data. Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-11-05 04:36 +0000
          Re: Algorithm that makes maximum compression of completly diffused data. Tim Roberts <timr@probo.com> - 2013-11-07 00:05 -0800
            Re: Algorithm that makes maximum compression of completly diffused data. Mark Janssen <dreamingforward@gmail.com> - 2013-11-07 10:59 -0800
            Re: Algorithm that makes maximum compression of completly diffused data. Tim Roberts <timr@probo.com> - 2013-11-07 11:22 -0800
            Re: Algorithm that makes maximum compression of completly diffused data. Chris Angelico <rosuav@gmail.com> - 2013-11-08 09:26 +1100
              Re: Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-11-07 18:05 -0800
                Re: Algorithm that makes maximum compression of completly diffused data. Chris Angelico <rosuav@gmail.com> - 2013-11-08 13:17 +1100
                Re: Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-11-07 18:25 -0800
                Re: Algorithm that makes maximum compression of completly diffused data. rusi <rustompmody@gmail.com> - 2013-11-07 18:36 -0800
                Re: Algorithm that makes maximum compression of completly diffused data. Chris Angelico <rosuav@gmail.com> - 2013-11-08 13:36 +1100
                Re: Algorithm that makes maximum compression of completly diffused data. Mark Janssen <dreamingforward@gmail.com> - 2013-11-07 18:43 -0800
                Re: Algorithm that makes maximum compression of completly diffused data. Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-11-08 04:47 +0000
                Re: Algorithm that makes maximum compression of completly diffused   data. Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2013-11-08 20:09 +1300
                Re: Algorithm that makes maximum compression of completly diffused data. Chris Angelico <rosuav@gmail.com> - 2013-11-08 18:21 +1100
                Re: Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-11-08 07:48 -0800
                Re: Algorithm that makes maximum compression of completly diffused data. rusi <rustompmody@gmail.com> - 2013-11-08 07:57 -0800
                Re: Algorithm that makes maximum compression of completly diffused data. Ian Kelly <ian.g.kelly@gmail.com> - 2013-11-08 11:48 -0700
                Re: Algorithm that makes maximum compression of completly diffused data. "R. Michael Weylandt <michael.weylandt@gmail.com>" <michael.weylandt@gmail.com> - 2013-11-07 21:43 -0500
                Re: Algorithm that makes maximum compression of completly diffused data. Chris Angelico <rosuav@gmail.com> - 2013-11-08 14:05 +1100
                Re: Algorithm that makes maximum compression of completly diffused data. Roy Smith <roy@panix.com> - 2013-11-07 22:08 -0500
                Re: Algorithm that makes maximum compression of completly diffused data. Chris Angelico <rosuav@gmail.com> - 2013-11-08 14:24 +1100
                Re: Algorithm that makes maximum compression of completly diffused data. "R. Michael Weylandt <michael.weylandt@gmail.com>" <michael.weylandt@gmail.com> - 2013-11-07 23:05 -0500
                Re: Algorithm that makes maximum compression of completly diffused data. Chris Angelico <rosuav@gmail.com> - 2013-11-08 15:06 +1100
                Re: Algorithm that makes maximum compression of completly diffused
 data. Dave Angel <davea@davea.name> - 2013-11-07 22:12 -0600
                Re: Algorithm that makes maximum compression of completly diffused data. Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2013-11-08 05:32 +0000
                Re: Algorithm that makes maximum compression of completly diffused data. Mark Janssen <dreamingforward@gmail.com> - 2013-11-07 18:24 -0800
                Re: Algorithm that makes maximum compression of completly diffused   data. Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2013-11-08 20:16 +1300
                Re: Algorithm that makes maximum compression of completly diffused data. Chris Angelico <rosuav@gmail.com> - 2013-11-08 13:27 +1100
      Re: Algorithm that makes maximum compression of completly diffused data. Ethan Furman <ethan@stoneleaf.us> - 2013-11-02 21:26 -0700
      Re: Algorithm that makes maximum compression of completly diffused data. Mark Janssen <dreamingforward@gmail.com> - 2013-11-02 23:09 -0700
      Re: Algorithm that makes maximum compression of completly diffused data. Michael Torrie <torriem@gmail.com> - 2013-11-03 08:14 -0700
    Re: Algorithm that makes maximum compression of completly diffused data. jonas.thornvall@gmail.com - 2013-10-30 12:49 -0700
  Re: Algorithm that makes maximum compression of completly diffused data. Grant Edwards <invalid@invalid.invalid> - 2013-10-30 21:18 +0000
  Re: Algorithm that makes maximum compression of completly diffused data. Mark Janssen <dreamingforward@gmail.com> - 2013-10-30 14:26 -0700
  Re: Algorithm that makes maximum compression of completly diffused data. Dave Angel <davea@davea.name> - 2013-10-31 03:22 +0000
  Re: Algorithm that makes maximum compression of completly diffused data. Gene Heskett <gheskett@wdtv.com> - 2013-11-03 04:50 -0500

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