Sampling binary contingency tables with a greedy start

  • Authors:

  • Ivona Bezáková;Nayantara Bhatnagar;Eric Vigoda

  • Affiliations:

  • Department of Computer Science, University of Chicago, Chicago, Illinois 60637;College of Computing, Georgia Institute of Technology, Atlanta, Georgia 30332;College of Computing, Georgia Institute of Technology, Atlanta, Georgia 30332

  • Venue:
  • Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
  • Year:
  • 2007

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Abstract

We study the problem of counting and randomly sampling binarycontingency tables. For given row and column sums, we areinterested in approximately counting (or sampling) 0/1 n xm matrices with the specified row/column sums. We present asimulated annealing algorithm with running timeO((nm)2D3dmax log 5(n + m)) for any row/columnsums, where D is the number of nonzero entries anddmax is the maximum row/column sum. In the worstcase, the running time of the algorithm isO(n11 log 5n) for ann x n matrix. This is the first algorithm to directlysolve binary contingency tables for all row/column sums. Previouswork reduced the problem to the permanent, or restricted attentionto row/column sums that are close to regular. The interestingaspect of our simulated annealing algorithm is that it starts at anontrivial instance, whose solution relies on the existence ofshort alternating paths in the graph constructed by a particularGreedy algorithm.© 2006 Wiley Periodicals, Inc. Random Struct.Alg., 2007