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A counterexample to rapid mixing of the Ge-Stefankovic process


 
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1. Title Title of document A counterexample to rapid mixing of the Ge-Stefankovic process
 
2. Creator Author's name, affiliation, country Leslie Ann Goldberg; University of Liverpool; United Kingdom
 
2. Creator Author's name, affiliation, country Mark Jerrum; Queen Mary, University of London; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Glauber dynamics; Independent sets in graphs; Markov chains; Mixing time; Randomised algorithms
 
3. Subject Subject classification 60J10 ; 05C31 ; 05C69 ; 68Q17
 
4. Description Abstract

Ge and Stefankovic have recently introduced a Markov chain which, if rapidly mixing, would provide an efficientprocedure for sampling independent sets in a bipartite graph. Such a procedure would be a breakthrough because it would give an efficient randomised algorithm for approximately counting independent sets in a bipartite graph, which would in turn imply the existence of efficient approximation algorithms for a number of significant counting problems whose computational complexity is so far unresolved. Their Markov chain is based on a novel two-variable graph polynomial which, when specialised to a bipartite graph, and evaluated at the point (1/2,1), givesthe number of independent sets in the graph. The Markov chain  is promising, in the sense that it overcomes the most obvious barrier to rapid mixing.  However, we show here, by exhibiting a sequence of counterexamples, that its mixing timeis  exponential in the size of the input when the input is chosen from a particular infinite family of bipartite graphs.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) EPSRC
 
7. Date (YYYY-MM-DD) 2012-01-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1712
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-1712
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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