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Faster Random Generation of Linear Extensions (1997)  (Make Corrections)  (22 citations)
Russ Bubley, Martin Dyer
Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms



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A tight bound on the mixing time of a non-trivial Markov chain.

Abstract: This paper examines the problem of sampling (almost) uniformly from the set of linear extensions of a partial order, a classic problem in the theory of approximate sampling. Previous techniques have relied on deep geometric arguments, or have not worked in full generality. Recently, focus has centred on the Karzanov and Khachiyan Markov chain. In this paper, we define a slightly different Markov chain, and present a very simple proof of its rapid mixing, using the method of path coupling. We... (Update)

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8:   A random polynomial time algorithm for approximating the volume of a convex body - Dyer, Frieze et al. - 1991
8:   Path coupling: A technique for proving rapid mixing in Markov chains (context) - Bubley, Dyer - 1997
7:   Counting linear extensions (context) - Brightwell, Winkler - 1991

BibTeX entry:   (Update)

R. Bubley and M. Dyer. Faster random generation of linear extensions. In Proceedings of the Ninth Annual ACM--SIAM Symposium on Discrete Algorithms, pages 175--186, San Francisco, CA, Jan 1998. http://citeseer.ist.psu.edu/bubley97faster.html   More

@inproceedings{ bubley98faster,
    author = "Russ Bubley and Martin Dyer",
    title = "Faster Random Generation of Linear Extensions",
    booktitle = "Proceedings of the Ninth Annual {ACM}-{SIAM} Symposium on Discrete Algorithms",
    month = "25--27",
    address = "San Francisco, California",
    pages = "350--354",
    year = "1998",
    url = "citeseer.ist.psu.edu/bubley97faster.html" }
Citations (may not include all citations):
113   Reversible Markov chains and random walks on graphs (context) - Aldous, Fill - 1994
98   A random polynomial-time algorithm for approximating the vol.. - Dyer, Frieze et al. - 1991
86   The Markov chain Monte Carlo method: an approach to approxim.. - Jerrum, Sinclair - 1996
73   uniform generation and rapidly mixing Markov chains (context) - Sinclair, Jerrum - 1989
49   Path coupling: A technique for proving rapid mixing in Marko.. (context) - Bubley, Dyer - 1997
43   Generating a random permutation with random transpositions (context) - Diaconis, Shahshahani - 1981
29   Computing the volume of convex bodies: A case where randomne.. - Dyer, Frieze - 1991
28   On Markov chains for independent sets - Dyer, Greenhill - 1997
26   Private Communication (context) - Wilson - 1997
23   the conductance of order Markov chains (context) - Karzanov, Khachiyan - 1991
23   Generating linear extensions fast - Pruesse, Ruskey - 1994
22   Counting linear extensions (context) - Brightwell, Winkler - 1991
21   Spearman's footrule as a measure of disarray (context) - Diaconis, Graham - 1977
19   Exact sampling with coupled Markov chains and applications t.. (context) - Propp, Wilson - 1996
10   Mixing times of lozenge tiling and card shuffling Markov cha.. (context) - Wilson - 1997
7   Markov chains for linear extensions (context) - Felsner, Wernisch - 1997
6   Footrule' for measuring correlations (context) - Spearman - 1906
5   Generating a random linear extension of a partial order (context) - Matthews - 1991
1   Definition of Spearman's footrule (context) - Dinneen, Blakesley - 1982



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