NDLI: Accelerating Simulated Annealing for the Permanent and Combinatorial Counting Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	tefankovi, Daniel Bezkov, Ivona Vazirani, Vijay V. Vigoda, Eric
Copyright Year	2008
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 (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.
Starting Page	1429
Ending Page	1454
Page Count	26
File Format	PDF
ISSN	00975397
DOI	10.1137/050644033
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	5
Volume Number	37
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2008-01-16
Access Restriction	Subscribed
Subject Keyword	approximate counting problems cooling schedule simulated annealing Markov chain Monte Carlo Randomized algorithms Approximation algorithms Analysis of algorithms
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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