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Random walks on truncated cubes and sampling 0-1 knapsack solutions

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2 Author(s)
Morris, B. ; Dept. of Stat., California Univ., Berkeley, CA, USA ; Sinclair, A.

We solve an open problem concerning the mixing time of a symmetric random walk on an n-dimensional cube truncated by a hyperplane, showing that it is polynomial in n. As a consequence, we obtain a full-polynomial randomized approximation scheme for counting the feasible solutions of a 0-1 knapsack problem. The key ingredient in our analysis is a combinatorial construction we call a “balanced almost uniform permutation”, which seems to be of independent interest

Published in:

Foundations of Computer Science, 1999. 40th Annual Symposium on

Date of Conference:

1999