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[Caml-list] Explaining bit sets
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Date: 2002-09-02 (20:17)
From: tim@f...
Subject: Re: [Caml-list] Holding a set of random integers of very wide range?
>For reasons I tried to explain in a previous draft of this e-mail and
>has been cut due to the amount of space it took, I need to generate
>multiple permuted lists of integers ranging from 0 to approximately
>2^100 (or more, it's a bit open-ended unfortunately).
>Since I only need one value at a time, I can use a lazy list for
>this. i.e., the head holds a value and the tail is a suspension of the
>state I need to generate the next value.  No big deal there.
>The big deal, for me anyways, is that the state I need is tracking the
>integers that I've already used (so that I don't generate the same one
>twice) given that the range of possible values is so large.

If your integers have enough bits, then a list of random numbers is
indistinguishable from a random permutation.  This assumes you only
have time to look at a reasonable number of values from the
permutation.  Do the math to figure out what "big enough" is.  For
example, in the past year I designed a scheme that assumed that two
files were identical if and only if their 64-bit checksums were
identical, and there were only a million or so files, so I did the
math and concluded that the chances of a collision were small enough.
It worked fine.

If you're paranoid then use the MD5 checksums in the Digest module to
generate random numbers; otherwise you can use a linear congruential
pseudo-random number generator as mentioned by another poster and hope
that there's no interesting interaction between the number generation
scheme and the other details of your algorithm.

>I'm currently using the very low-tech solution of maintaining a list
>of ranges of used values.  (i.e., when I use a value that would link 2
>different ranges, I go coalesce the list.  The worst case would be if
>I picked all the odd integers or all the even integers.)
>Given the recent talk of Patricia trees and bit sets, I was wondering
>if some variant of either one of those, or some other representation
>would be better for what I'm doing?  (I figure at the very least I
>ought to be using a tree of ranges of used values.  I'm currently
>using the Big_int module to represent my integers.)

If your integers are large enough, then you can ignore the possiblity
of a collision and no data structure is needed.  Otherwise, is there a
reason not to use a hash table?  

Tim Freeman       
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