SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A Deterministic Polynomial-Time Approximation Scheme for Counting Knapsack Solutions
SIAM Journal on Computing
Hardness results for the probabilistic traveling salesman problem with deadlines
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Time hierarchies for sampling distributions
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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We solve an open problem concerning the mixing time of symmetric random walk on the n-dimensional cube truncated by a hyperplane, showing that it is polynomial in n. As a consequence, we obtain a fully polynomial randomized approximation scheme for counting the feasible solutions of a 0-1 knapsack problem. The results extend to the case of any fixed number of hyperplanes. The key ingredient in our analysis is a combinatorial construction we call a "balanced almost uniform permutation," which is of independent interest.