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Abstract

This paper addresses the problem of sampling contingency tables (non-negative integer matrices with specified row and column sums) uniformly at random. We give an approximation algorithm which runs in polynomial time provided that the row and column sums satisfy r i =Ω (n 3/2 m log(m)), and c j =Ω (m 3/2 n log(n)). Our algorithm is based on a reduction to continuous sampling from a convex set. This is an approach which was taken by Dyer, Kannan and Mount in previous work. However, the algorithm we present is simpler, and has a greater range of applicability since the requirements on the row and column sums are weaker.

Keywords

Contingency Table Integer Point Integer Matrix 25th International Colloquium Improve Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Diaconis, P., Efron, B.: Testing for independence in a two-way table: new interpre- tations of the chi-squared statististic. Annals of Statistics 13, 845–913 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Dyer, M.E., Frieze, A.M., Kannan, R.: A random polynomial time algorithm for approximating the volume of convex bodies. Journal of the ACM 38, 1–17 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Dyer, M.E., Greenhill, C.: A genuinely polynomial-time algorithm for sampling two-rowed contingency tables. In: Proceedings of the 25th International Colloquium on Automata, Languages and Programming, pp. 339–350 (1998)Google Scholar
  4. 4.
    Dyer, M.E., Kannan, R., Mount, J.: Sampling contingency tables. Random Structures & Algorithms 10, 487–506 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Kannan, R., Lovász, L.: A logarithmic Cheeger inequality and mixing in random walks. In: Proceedings of ACM Symposium on Theory of Computing (1999) (to appear)Google Scholar
  6. 6.
    Kannan, R., Lovász, L., Simonovits, M.: Random walks and an O*(n5) volume algorithm for convex bodies. Random Structures & Algorithms 11, 1–50 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kannan, R., Vempala, S.: Sampling Lattice Points. In: Proceedings of the 29th Annual Symposium on the Theory of Computing, pp. 696–700 (1997)Google Scholar
  8. 8.
    Lovász, L.: Hit and run mixes fast, Yale University, New Haven (1998) (Preprint)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Ben Morris
    • 1
  1. 1.Statistics DepartmentUniversity of CaliforniaBerkeleyUSA

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