The bipartite travelling salesman problem: A pyramidally solvable case

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

Operations Research Letters Pub Date : 2024-05-27 DOI:10.1016/j.orl.2024.107130

Vladimir G. Deineko , Bettina Klinz , Gerhard J. Woeginger

引用次数: 0

Abstract

Given k blue cities, k red cities and a $2 k \times 2 k$ distance matrix, the task in the bipartite travelling salesman problem is to find a shortest tour which alternately visits blue and red cities. We consider the special case of Van der Veen distance matrices and show that it remains NP-hard in general but can be solved in $O (k^{2})$ time when all vertices with odd indices are blue and all with even indices are red.

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二方旅行推销员问题：金字塔式可解案例

给定 k 个蓝色城市、k 个红色城市和一个 2k×2k 的距离矩阵，两方旅行推销员问题的任务是找到一个交替访问蓝色和红色城市的最短旅行路线。我们考虑了范德维恩距离矩阵的特殊情况，并证明该问题在一般情况下仍然是 NP 难题，但当所有奇数索引的顶点都是蓝色，偶数索引的顶点都是红色时，该问题可以在 O(k2) 时间内求解。

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

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.