Accelerating Simulated Annealing for the Permanent and Combinatorial Counting Problems Ivona BezÂ´kovÂ´ a a Abstract 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 (di cult 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(n7 log4 n) time algorithm for approximating the permanent of a 0/1 matrix. 1 Introduction Simulated annealing is an important algorithmic approach for counting and sampling combinatorial structures. Two notable combinatorial applications are estimating the partition function of statistical physics models, and approximating the permanent of a non-negative matrix. For combinatorial counting problems, the general idea of simulated annealing is to write the desired quantity, say Z, (which is, for example, the number of colorings or matchings of an input graph) as a telescoping
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