A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents

Nathan Linial*, Alex Samorodnitsky, Avi Wigderson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

92 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 simple new (slow) polynomial time decision algorithm for bipartite perfect matching, conceptually different from classical approaches.

Original languageAmerican English
Pages (from-to)545-568
Number of pages24
JournalCombinatorica
Volume20
Issue number4
DOIs
StatePublished - 2000

Bibliographical note

Funding Information:
∗ Work supported in part by a grant of th e Binational Israel-US Science Foundation. † Work partially supported by grant 032-7736 from th e Israel Academy of Sciences. Part of th is work was done during a visit to th e Institute for Advanced Study, under th e support of a Sloan Foundation grant 96-6-2.

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