Deterministic strongly polynomial algorithm for matrix scaling and approximate permanents

Nathan Linial; Alex Samorodnitsky; Avi Wigderson

Deterministic strongly polynomial algorithm for matrix scaling and approximate permanents

Nathan Linial^*
, Alex Samorodnitsky
, Avi Wigderson

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Conference article › peer-review

52 Scopus citations

Abstract

We present a deterministic strongly polynomial algorithm that computes the permanent of a nonnegative n×n matrix to within a multiplicative factor of eⁿ. 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 (slow) decision algorithm for bipartite perfect matching, conceptually different from known approaches.

Original language	English
Pages (from-to)	644-652
Number of pages	9
Journal	Conference Proceedings of the Annual ACM Symposium on Theory of Computing
State	Published - 1998
Event	Proceedings of the 1998 30th Annual ACM Symposium on Theory of Computing - Dallas, TX, USA Duration: 23 May 1998 → 26 May 1998

Cite this

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title = "Deterministic strongly polynomial algorithm for matrix scaling and approximate permanents",

abstract = "We present a deterministic strongly polynomial algorithm that computes the permanent of a nonnegative n{\texttimes}n matrix to within a multiplicative factor of en. 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 (slow) decision algorithm for bipartite perfect matching, conceptually different from known approaches.",

author = "Nathan Linial and Alex Samorodnitsky and Avi Wigderson",

year = "1998",

language = "אנגלית",

pages = "644--652",

journal = "Conference Proceedings of the Annual ACM Symposium on Theory of Computing",

issn = "0734-9025",

publisher = "Association for Computing Machinery",

note = "Proceedings of the 1998 30th Annual ACM Symposium on Theory of Computing ; Conference date: 23-05-1998 Through 26-05-1998",

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AU - Linial, Nathan

AU - Samorodnitsky, Alex

AU - Wigderson, Avi

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N2 - We present a deterministic strongly polynomial algorithm that computes the permanent of a nonnegative n×n matrix to within a multiplicative factor of en. 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 (slow) decision algorithm for bipartite perfect matching, conceptually different from known approaches.

AB - We present a deterministic strongly polynomial algorithm that computes the permanent of a nonnegative n×n matrix to within a multiplicative factor of en. 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 (slow) decision algorithm for bipartite perfect matching, conceptually different from known approaches.

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AN - SCOPUS:0031619018

SN - 0734-9025

SP - 644

EP - 652

JO - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

JF - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

T2 - Proceedings of the 1998 30th Annual ACM Symposium on Theory of Computing

Y2 - 23 May 1998 through 26 May 1998

ER -

Deterministic strongly polynomial algorithm for matrix scaling and approximate permanents

Abstract

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