Random generation of combinatorial structures from a uniform
Theoretical Computer Science
How hard is it to marry at random? (On the approximation of the permanent)
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
SIAM Journal on Computing
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
A very simple algorithm for estimating the number of k-colorings of a low-degree graph
Random Structures & Algorithms
Tracking Many Objects with Many Sensors
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Path coupling: A technique for proving rapid mixing in Markov chains
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
A Non-Markovian Coupling for Randomly Sampling Colorings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Simulated Annealing in Convex Bodies and an 0*(n4) Volume Algorithm
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Sampling binary contingency tables with a greedy start
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Negative examples for sequential importance sampling of binary contingency tables
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Fast approximation of the permanent for very dense problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A dynamic programming approach to efficient sampling from Boltzmann distributions
Operations Research Letters
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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(n7 log4 n) time algorithm for approximating the permanent of a 0/1 matrix.