Bipartite Perfect Matching as a Real Polynomial

被引：4

作者：

Beniamini, Gal ^{[1
]}

Nisan, Noam ^{[1
]}

机构：

[1] Hebrew Univ Jerusalem, Jerusalem, Israel

来源：

STOC '21: PROCEEDINGS OF THE 53RD ANNUAL ACM SIGACT SYMPOSIUM ON THEORY OF COMPUTING | 2021年

基金：

欧洲研究理事会;

关键词：

Bipartite Perfect Matching; Boolean Functions; Elementary Graphs;

D O I：

10.1145/3406325.3451002

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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 - o(n)(1)) . 2(n2) 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 Theta(n log n). Our proof relies heavily on the fact that the lattice of graphs which are "matching-covered" is Eulerian.

引用

页码：1118 / 1131

页数：14

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