A MILP model for the connected multidimensional maximum bisection problem

IF 0.9 4区数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Combinatorial Optimization Pub Date : 2024-10-22 DOI:10.1007/s10878-024-01220-z

Zoran Lj. Maksimović

引用次数: 0

Abstract

The Maximum Bisection Problem (MBP) is a well-known combinatorial optimization problem that has been proven to be NP-hard. The maximum bisection of a graph is the partition of its set of vertices into two subsets with an equal number of vertices, where the weight of the edge cut is maximal. This work introduces a connected multidimensional generalization of the Maximum Bisection Problem. In this NP-hard problem, weights on edges are vectors of non-negative numbers, and subgraphs induced by partitions must be connected. A mixed integer linear programming (MILP) formulation is proposed with proof of its correctness. The MILP formulation of the problem has a polynomial number of variables and constraints

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连通多维最大分割问题的 MILP 模型

最大分割问题（MBP）是一个著名的组合优化问题，已被证明为 NP 难。图的最大分割是将图的顶点集分割成顶点数相等的两个子集，其中切边的权重最大。这项研究引入了最大分割问题的多维连接广义。在这个 NP 难问题中，边上的权重是非负数向量，分区诱导的子图必须是相连的。我们提出了一个混合整数线性规划（MILP）公式，并证明了其正确性。该问题的 MILP 公式具有多项式数量的变量和约束条件

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

Journal of Combinatorial Optimization 数学-计算机：跨学科应用

CiteScore

2.00

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering. The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.