## Random walks on combinatorial objects (1999)

Venue: | Surveys in Combinatorics 1999 |

Citations: | 25 - 8 self |

### BibTeX

@INPROCEEDINGS{Dyer99randomwalks,

author = {Martin Dyer and Catherine Greenhill},

title = {Random walks on combinatorial objects},

booktitle = {Surveys in Combinatorics 1999},

year = {1999},

pages = {101--136},

publisher = {University Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

Summary Approximate sampling from combinatorially-defined sets, using the Markov chain Monte Carlo method, is discussed from the perspective of combinatorial algorithms. We also examine the associated problem of discrete integration over such sets. Recent work is reviewed, and we re-examine the underlying formal foundational framework in the light of this. We give a detailed treatment of the coupling technique, a classical method for analysing the convergence rates of Markov chains. The related topic of perfect sampling is examined. In perfect sampling, the goal is to sample exactly from the target set. We conclude with a discussion of negative results in this area. These are results which imply that there are no polynomial time algorithms of a particular type for a particular problem. 1