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Latin American Symposium on Theoretical Informatics

LATIN 1998: LATIN'98: Theoretical Informatics pp 292–304Cite as

Analyzing Glauber dynamics by comparison of Markov chains

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1380))

Abstract

A popular technique for studying random properties of a combinatorial set is to design a Markov chain Monte Carlo algorithm. For many problems there are natural Markov chains connecting the set of allowable configurations which are based on local moves, or “Glauber dynamics.” Typically these single site update algorithms are difficult to analyze, so often the Markov chain is modified to update several sites simultaneously. Recently there has been progress in analyzing these more complicated algorithms for several important combinatorial problems.

In this work we use the comparison technique of Diaconis and Saloff-Coste to show that several of the natural single point update algorithms are efficient. The strategy is to relate the mixing rate of these algorithms to the corresponding non-local algorithms which have already been analyzed. This allows us to give polynomial bounds for single point update algorithms for problems such as generating tilings, colorings and independent sets.

Research supported by NSF Grants No. CCR-9703206 and CCR-9503952.

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Author information

Authors and Affiliations

  1. School of Mathematics and College of Computing, Georgia Institute of Technology, 30332, Atlanta, GA, USA

    Dana Randall

  2. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, GA, USA

    Prasad Tetali

Authors
  1. Dana Randall
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  2. Prasad Tetali
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Editor information

Cláudio L. Lucchesi Arnaldo V. Moura

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© 1998 Springer-Verlag Berlin Heidelberg

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Randall, D., Tetali, P. (1998). Analyzing Glauber dynamics by comparison of Markov chains. In: Lucchesi, C.L., Moura, A.V. (eds) LATIN'98: Theoretical Informatics. LATIN 1998. Lecture Notes in Computer Science, vol 1380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054330

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  • DOI: https://doi.org/10.1007/BFb0054330

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64275-6

  • Online ISBN: 978-3-540-69715-2

  • eBook Packages: Springer Book Archive

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