Sampling binary contingency tables with a greedy start

  1. Ivona Bezáková1,
  2. Nayantara Bhatnagar2,
  3. Eric Vigoda2,*

Article first published online: 13 DEC 2006

DOI: 10.1002/rsa.20155

Issue

Random Structures & Algorithms

Random Structures & Algorithms

Special Issue: Proceedings from the 12th International Conference “Random Structures and Algorithms”, August 1–5, 2005, Poznan, Poland. Dedicated to Alan Frieze on the occasion of his 60th birthday

Volume 30, Issue 1-2, pages 168–205, January - March 2007

Additional Information

How to Cite

Bezáková, I., Bhatnagar, N. and Vigoda, E. (2007), Sampling binary contingency tables with a greedy start. Random Struct. Alg., 30: 168–205. doi: 10.1002/rsa.20155

Author Information

  1. 1

    Department of Computer Science, University of Chicago, Chicago, Illinois 60637

  2. 2

    College of Computing, Georgia Institute of Technology, Atlanta, Georgia 30332

*College of Computing, Georgia Institute of Technology, Atlanta, Georgia 30332

Publication History

  1. Issue published online: 27 DEC 2006
  2. Article first published online: 13 DEC 2006
  3. Manuscript Accepted: 11 OCT 2006
  4. Manuscript Received: 8 OCT 2005

Funded by

  • NSF. Grant Number: CCR-0455666

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Keywords:

  • Markov chain;
  • Monte Carlo;
  • contingency tables;
  • approximate counting;
  • simulated annealing

Abstract

We study the problem of counting and randomly sampling binary contingency tables. For given row and column sums, we are interested in approximately counting (or sampling) 0/1 n × m matrices with the specified row/column sums. We present a simulated annealing algorithm with running time O((nm)2D3dmax log 5(n + m)) for any row/column sums, where D is the number of nonzero entries and dmax is the maximum row/column sum. In the worst case, the running time of the algorithm is O(n11 log 5n) for an n × n matrix. This is the first algorithm to directly solve binary contingency tables for all row/column sums. Previous work reduced the problem to the permanent, or restricted attention to row/column sums that are close to regular. The interesting aspect of our simulated annealing algorithm is that it starts at a nontrivial instance, whose solution relies on the existence of short alternating paths in the graph constructed by a particular Greedy algorithm.© 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007

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