Bipartite perfect matching as a real polynomial

Gal Beniamini; Noam Nisan

doi:10.1145/3406325.3451002

Bipartite perfect matching as a real polynomial

Gal Beniamini, Noam Nisan

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

8 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 language	English
Title of host publication	STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
Editors	Samir Khuller, Virginia Vassilevska Williams
Publisher	Association for Computing Machinery
Pages	1118-1131
Number of pages	14
ISBN (Electronic)	9781450380539
DOIs	https://doi.org/10.1145/3406325.3451002
State	Published - 15 Jun 2021
Event	53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy Duration: 21 Jun 2021 → 25 Jun 2021

Publication series

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

Conference

Conference	53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Country/Territory	Italy
City	Virtual, Online
Period	21/06/21 → 25/06/21

Bibliographical note

Publisher Copyright:
© 2021 ACM.

Keywords

Bipartite Perfect Matching
Boolean Functions
Elementary Graphs

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10.1145/3406325.3451002

Cite this

Beniamini, G., & Nisan, N. (2021). Bipartite perfect matching as a real polynomial. In S. Khuller, & V. V. Williams (Eds.), STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing (pp. 1118-1131). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/3406325.3451002

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Beniamini, G & Nisan, N 2021, Bipartite perfect matching as a real polynomial. in S Khuller & VV Williams (eds), STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 1118-1131, 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021, Virtual, Online, Italy, 21/06/21. https://doi.org/10.1145/3406325.3451002

Bipartite perfect matching as a real polynomial. / Beniamini, Gal; Nisan, Noam.
STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. ed. / Samir Khuller; Virginia Vassilevska Williams. Association for Computing Machinery, 2021. p. 1118-1131 (Proceedings of the Annual ACM Symposium on Theory of Computing).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Bipartite perfect matching as a real polynomial

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