| Título: | A counterexample to rapid mixing of the Ge-Stefankovic process |
| Autores: |
Goldberg, Leslie Ann; University of Liverpool Jerrum, Mark; Queen Mary, University of London |
| Fecha: | 2012-01-02 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
Glauber dynamics; Independent sets in graphs; Markov chains; Mixing time; Randomised algorithms 60J10 ; 05C31 ; 05C69 ; 68Q17 |
| Descripción: | 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. |
| Idioma: | Inglés |
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