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### Re^3: Data compression by 50% + : is it possible?

by BrowserUk (Pope)
 on May 12, 2019 at 01:52 UTC ( #1233626=note: print w/replies, xml ) Need Help??

It makes a small -- insignificant -- difference to the outcome.

A quick check -- because quicker than trying to derive a formula -- shows that of the 729,000 3-value combinations, 11,839 contain consecutive numbers:

```use Algorithm::Combinatorics qw[ variations_with_repetition ];;

@c = variations_with_repetition( [ 1 .. 90 ], 3 );;
print scalar @c;;
729000

\$d = 0; \$_->[0]+1 == \$_->[1] or \$_->[1]+1 == \$_->[2] and ++\$d for @c;
+print \$d;;
7922

And there are 8010 combinations of 2 sets of three that must be excluded because the last digit of the first set of 3 is one less that the first digit of the second set:

```\$d = 0; \$_->[0] == \$_->[2]+1 and ++\$d for @c; print \$d;;
8010

Which means that instead of 531,441,000,000 6-value combinations, there are only (729,000 - 7922 )**2 - 8010 = 519,953,474,074, which means it would still take 40-bits to represent any legal 6-value string; so the math doesn't change: ( 1 - 40/48 ) *100 = 16.67% is best possible for *any* dataset.

Any algorithm that achieves better on any given dataset; will not achieve the same results for all datasets; nor even a high percentage of them.

Ie. To achieve better, you'd need to reduce the size of the domain so that you could compress 36-bits into 48 which would give 25% compression. But that would require throwing away 87% of the possible datasets

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority". The enemy of (IT) success is complexity.
In the absence of evidence, opinion is indistinguishable from prejudice. Suck that fhit

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Re^4: Data compression by 50% + : is it possible?
by roboticus (Chancellor) on May 12, 2019 at 13:07 UTC

There are remarkably fewer combinations than it would appear at first glance. The OP creates a vector of four random digits (0..9), but then enforces a few rules:

• The four digits are sorted: This reduces 10,000 input vectors to 715 possible outputs.
• Then the code eliminates duplicate values and sequential values reducing the 715 inputs to 102 outputs.
• Then the first value is removed from the list reducing the possible outputs to 50.

As a result of those rules, none of the output groups will contain 0 or 1. So with the OPs script, you should never see the characters:

```\$ perl -e 'print join(" ", map { chr(33+\$_), chr(33+\$_+1) } map {10*\$_
+} 0 .. 8)'
! " + , 5 6 ? @ I J S T ] ^ g h q r

That removes 18 of the 90 values, greatly reducing the number of possible records generated. Additionally, the remaining digits aren't equally distributed: 2 appears about half as often as 3 and about a third as often as 9.

...roboticus

When your only tool is a hammer, all problems look like your thumb.

So with the OPs script, ... that removes 18 of the 90 values,

And do you think that is his intent, or just clumsy coding? Has he said?

Additionally, the remaining digits aren't equally distributed: 2 appears about half as often as 3 and about a third as often as 9.

Again, is that a carefully designed intent, or just a badly coded demo thrown together for posting? Is true regardless of whether he uses the same PRNG as you tested?

Didn't he say preserving order was a goal, even if not a requirement? With does he mean the order before or after that sort in the demo code?

Even if the reduction to 72 values, is intended, you still get ( 1 - 6.16992500144231 / 8 ) *100 = 22.875937481971125% best possible saving.

If you take his description as the 'spec', as I did, -- rather then the output of a few trials of his code on a given machine/PRNG as you have -- the answer to his title question: "Data compression by 50% + : is it possible?", is: no.

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority". The enemy of (IT) success is complexity.
In the absence of evidence, opinion is indistinguishable from prejudice. Suck that fhit
Just to make it clear, there is no clumsy coding. Clumsy wording maybe, but no coding. That is why i posted the code instead trying to describe it. But I do understand the point you are trying to convey. Thnx!

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