A Deterministic Strongly Polynomial Algorithm for Matrix Scaling and Approximate Permanents

Combinatorica volume 20, pages545–568(2000)Cite this article

matrix to within a multiplicative factor of . To this end we develop the first strongly polynomial-time algorithm for matrix scaling –– an important nonlinear optimization problem with many applications. Our work suggests a simple new (slow) polynomial time decision algorithm for bipartite perfect matching, conceptually different from classical approaches.

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Affiliations

  1. School of Computer Science and Engeneering, The Hebrew University; Jerusalem 91904, Israel; E-mail: nati@cs.huji.ac.il, IL

    Nathan Linial

  2. School of Mathematics, Institute for Advanced Study; Princeton, NJ 08540, U.S.A.; E-mail: asamor@ias.edu, US

    Alex Samorodnitsky

  3. School of Mathematics, Institute for Advanced Study; Princeton, NJ 08540, U.S.A.; and School of Computer Science and Engineering; The Hebrew University; Jerusalem, 91904, Israel; E-mail: avi@ias.edu, US

    Avi Wigderson

Authors
  1. Nathan Linial
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  2. Alex Samorodnitsky
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  3. Avi Wigderson
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Received October 15, 1998

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Linial, N., Samorodnitsky, A. & Wigderson, A. A Deterministic Strongly Polynomial Algorithm for Matrix Scaling and Approximate Permanents. Combinatorica 20, 545–568 (2000). https://doi.org/10.1007/s004930070007

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  • AMS Subject Classification (1991) Classes:  90C27, 15A15, 15A12, 90C30, 65B99