The time complexity of maximum matching by simulated annealing
Journal of the ACM (JACM)
The effect of the density of states on the Metropolis algorithm
Information Processing Letters
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
Simulated annealing for graph bisection
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Simulated annealing beats metropolis in combinatorial optimization
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Using markov-chain mixing time estimates for the analysis of ant colony optimization
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Information Processing Letters
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This paper focusses on the performance of the Metropolis algorithm when employed for solving combinatorial optimization problems. One finds in the literature two notions of success for the Metropolis algorithm in the context of such problems. First, we show that both these notions are equivalent. Next, we provide two characterizations, or in other words, necessary and sufficient conditions, for the success of the algorithm, both characterizations being conditions on the family of Markov chains which the Metropolis algorithm gives rise to when applied to an optimization problem. The first characterization is that the Metropolis algorithm is successful if in every chain, for every set A of states not containing the optimum, the ratio of the ergodic flow out of A to the capacity of A is high. The second characterization is that in every chain the stationary probability of the optimum is high and that the family of chains mixes rapidly. We illustrate the applicability of our results by giving alternative proofs of certain known results.