Bipartite perfect matching as a real polynomial

Gal Beniamini, Noam Nisan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

We obtain a description of the Bipartite Perfect Matching decision problem as a multilinear polynomial over the Reals. We show that it has full degree and (1-on(1))· 2n2 monomials with non-zero coefficients. In contrast, we show that in the dual representation (switching the roles of 0 and 1) the number of monomials is only exponential in I(n logn). Our proof relies heavily on the fact that the lattice of graphs which are "matching-covered"is Eulerian.

Original languageAmerican English
Title of host publicationSTOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
EditorsSamir Khuller, Virginia Vassilevska Williams
PublisherAssociation for Computing Machinery
Pages1118-1131
Number of pages14
ISBN (Electronic)9781450380539
DOIs
StatePublished - 15 Jun 2021
Event53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy
Duration: 21 Jun 202125 Jun 2021

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Country/TerritoryItaly
CityVirtual, Online
Period21/06/2125/06/21

Bibliographical note

Publisher Copyright:
© 2021 ACM.

Keywords

  • Bipartite Perfect Matching
  • Boolean Functions
  • Elementary Graphs

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