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A Permanent Algorithm with exp[Ω (n ^{1/3}/2 ln n )] Expected Speedup for 0-1 Matrices

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Abstract

This paper outlines a permanent algorithm with mildly exponential expected speedup over Ryser's inclusion and exclusion algorithm for 0-1 matrices. The algorithm is based on a finite-difference formula that is a generalization of Ryser's formula. The matrix is augmented by a column of entries selected to produce zero-valued terms in the formula. The algorithm achieves speedup by avoiding computation of many zero-valued terms.

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Authors and Affiliations

  1. PO Box 60543, Pasadena, CA 91116-6543, USA. eric@cs.caltech.edu., US

    Bax

  2. Department of Applied Mathematics, California Institute of Technology 217-50, Pasadena, CA 91125, USA. jnf@ama.caltech.edu., US

    Franklin

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  1. Bax
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  2. Franklin
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Bax, Franklin A Permanent Algorithm with exp[Ω (n ^{1/3}/2 ln n )] Expected Speedup for 0-1 Matrices . Algorithmica 32, 157–162 (2002). https://doi.org/10.1007/s00453-001-0072-0

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  • DOI: https://doi.org/10.1007/s00453-001-0072-0

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