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Re^2: Random Math Question

by sk (Curate)
on Oct 11, 2005 at 05:43 UTC ( #499036=note: print w/replies, xml ) Need Help??

in reply to Re: Random Math Question
in thread Random Math Question

blokhead, Thanks for all the wonderful explanations.

    Let's for this discussion assume that all we need is an algorithm that can potentially produce every p! permutation of a sequence (1..p)

I was wondering whether a two dimensional shuffling (not sure if that is the right term) would help us achieve such a suffle without having to resort to a random variable with entropy 1516705 bits. Here are the steps i have in mind -

1. Partition the sequence into k-lists (each list containing n-elements) and that each list can be truly randomized. Also WLOG let's assume k <= n

2. For all i 1 to n and j = 1 to k,

  a. generate integers (X,Y) ~ U from the planar region bounded by x = n and y = k.

  b. Now we swap element(i,j) with element(X,Y).

Since each (i,j) is equally likely => i*n+j is equally likely. Is there anything wrong with this approach?




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