Mixing Time of Markov chain of the Knapsack Problem

03/11/2018

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by   Koko K. Kayibi, et al.

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To find the number of assignments of zeros and ones satisfying a specific Knapsack Problem is #P hard, so only approximations are envisageable. A Markov chain allowing uniform sampling of all possible solutions is given by Luby, Randall and Sinclair. In 2005, Morris and Sinclair, by using a flow argument, have shown that the mixing time of this Markov chain is O(n^9/2+ϵ), for any ϵ > 0. By using a canonical path argument on the distributive lattice structure of the set of solutions, we obtain an improved bound, the mixing time is given as τ__x(ϵ) ≤ n^3 (16 ϵ^-1).