The Bipartite Boolean Quadric Polytope

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2022-05-01 DOI:10.1016/j.disopt.2021.100657

Piyashat Sripratak , Abraham P. Punnen , Tamon Stephen

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引用次数: 5

Abstract

We consider the Bipartite Boolean Quadratic Programming Problem (BQP01), which generalizes the well-known Boolean quadratic programming problem (QP01). The model has applications in graph theory, matrix factorization and bioinformatics, among others. The primary focus of this paper is on studying the structure of the Bipartite Boolean Quadric Polytope (BQP $^{m, n}$ ) resulting from a linearization of a quadratic integer programming formulation of BQP01.

We present some basic properties and partial relaxations of BQP $^{m, n}$ , as well as some families of facets and valid inequalities. We find facet-defining inequalities including a family of odd-cycle inequalities. We discuss various approaches to obtain a valid inequality and facets from those of the related Boolean quadric polytope. The key strategy is based on rounding coefficients, and it is applied to the families of clique and cut inequalities in BQP $^{m, n}$ .

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二部布尔二次多边形

我们考虑二部布尔二次规划问题(BQP01)，它推广了著名的布尔二次规划问题(QP01)。该模型在图论、矩阵分解和生物信息学等领域具有广泛的应用。本文主要研究了由BQP01的二次整数规划公式线性化而得到的二部布尔二次多边形(BQPm,n)的结构。给出了BQPm,n的一些基本性质和部分松弛，以及一些平面族和有效不等式。我们发现面定义不等式包括奇循环不等式族。讨论了从相关布尔二次多边形的不等式和面中获得有效不等式和面的各种方法。关键策略是基于舍入系数的，并将其应用于BQPm中的团不等式和切不等式族。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.