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ICALP
2004
Springer

Simple Permutations Mix Well

13 years 9 months ago
Simple Permutations Mix Well
We study the random composition of a small family of O(n3 ) simple permutations on {0, 1}n . Specifically we ask what is the number of compositions needed to achieve a permutation that is close to k-wise independent. We improve on a result of Gowers [7] and show that up to a polylogarithmic factor, n3 k3 compositions of random permutations from this family suffice. Additionally, we introduce a new notion analogous to closeness to k-wise independence against adaptive adversaries and show the constructed permutation has the stronger property. This question is essentially about the rapid mixing of the random walk on a certain graph which we establish using a new approach to construct the so called canonical paths, which may be of independent interest. We also show that if we are willing to use a much larger family of simple permutations then we can guaranty closeness to k-wise independence with fewer compositions and fewer random bits.
Shlomo Hoory, Avner Magen, Steven Myers, Charles R
Added 01 Jul 2010
Updated 01 Jul 2010
Type Conference
Year 2004
Where ICALP
Authors Shlomo Hoory, Avner Magen, Steven Myers, Charles Rackoff
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