Random Structures & Algorithms
Adaptive simulated annealing: A near-optimal connection between sampling and counting
Journal of the ACM (JACM)
Sampling Eulerian orientations of triangular lattice graphs
Journal of Discrete Algorithms
Efficient circuits for quantum walks
Quantum Information & Computation
Submodular maximization by simulated annealing
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Hitting time of quantum walks with perturbation
Quantum Information Processing
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We present an improved “cooling schedule” for simulated annealing algorithms for combinatorial counting problems. Under our new schedule the rate of cooling accelerates as the temperature decreases. Thus, fewer intermediate temperatures are needed as the simulated annealing algorithm moves from the high temperature (easy region) to the low temperature (difficult region). We present applications of our technique to colorings and the permanent (perfect matchings of bipartite graphs). Moreover, for the permanent, we improve the analysis of the Markov chain underlying the simulated annealing algorithm. This improved analysis, combined with the faster cooling schedule, results in an $O(n^7\log^4{n})$ time algorithm for approximating the permanent of a $0/1$ matrix.