最小和着色问题的ILP模型和列生成

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-02-01 DOI:10.1016/j.endm.2018.01.023

Fabio Furini, Enrico Malaguti , Sébastien Martin, Ian-Christopher Ternier

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引用次数: 7

摘要

研究了最小和着色问题(MSCP)的两个整数线性规划(ILP)公式。该问题是经典顶点着色问题的扩展，其中每种颜色都由一个正自然数表示。MSCP要求最小化接收相同颜色的顶点子集的基数之和，并通过颜色的索引进行加权，同时确保由边缘连接的顶点接收不同的颜色。第一个ILP公式具有多项式数量的变量，而第二个ILP公式具有指数数量的变量，并通过列生成来解决。计算试验表明，第二种形式的线性规划松弛提供了紧的下界，使我们能够求解文献中一些难以证明的最优性实例。

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ILP Models and Column Generation for the Minimum Sum Coloring Problem

We study two Integer Linear Programming (ILP) formulations for the Minimum Sum Coloring Problem (MSCP). The problem is an extension of the classical Vertex Coloring Problem in which each color is represented by a positive natural number. The MSCP asks to minimize the sum of the cardinality of subsets of vertices receiving the same color, weighted by the index of the color, while ensuring that vertices linked by an edge receive different colors. The first ILP formulation has a polynomial number of variables while the second one has an exponential number of variables and is tackled via column generation. Computational tests show that the linear programming relaxation of the second formulation provides tight lower bounds which allow us to solve to proven optimality some hard instances of the literature.

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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.