以顶点覆盖数为参数的旅行推销员问题的二次阶问题内核

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2024-01-01 DOI:10.1016/j.orl.2024.107065

René van Bevern , Daniel A. Skachkov

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引用次数: 0

摘要

图形旅行推销员问题（NP-hard graphical traveling salesman problem，GTSP）是指找到一个总重量最小的封闭步行路径，该路径能访问无向有边加权且不一定完整的图中的每个顶点。我们为 GTSP 提出了一个具有 τ2+τ 个顶点的问题内核，其中 τ 是输入图的顶点覆盖数。对于任意 α≥1 的问题内核，任何 α 近似解都能给出原始实例的 α 近似解。

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A quadratic-order problem kernel for the traveling salesman problem parameterized by the vertex cover number

The NP-hard graphical traveling salesman problem (GTSP) is to find a closed walk of total minimum weight that visits each vertex in an undirected edge-weighted and not necessarily complete graph. We present a problem kernel with $τ^{2} + τ$ vertices for GTSP, where τ is the vertex cover number of the input graph. Any α-approximate solution for the problem kernel also gives an α-approximate solution for the original instance, for any $α \geq 1$ .

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

期刊介绍： Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.