Circulant TSP special cases: Easily-solvable cases and improved approximations

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

Operations Research Letters Pub Date : 2024-05-31 DOI:10.1016/j.orl.2024.107133

Austin Beal, Yacine Bouabida, Samuel C. Gutekunst, Asta Rustad

引用次数: 0

Abstract

Circulant TSP is an intriguing special case of the Traveling Salesman Problem, whose complexity remains an often-cited open problem. In this note, we present three results: We show that circulant TSP can be efficiently solved whenever the input number of vertices is a prime-squared; we show that the ${1, 2}$ -TSP can be easily and efficiently solved when specialized to circulant instances; and we present a substantially-improved approximation factor for finding a minimum-cost Eulerian connected sub-(multi)graph on two-stripe circulant instances.

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循环 TSP 特殊情况：易于解决的案例和改进的近似值

圆周率 TSP 是旅行推销员问题的一个有趣特例，其复杂性仍是一个经常被引用的未决问题。在本论文中，我们提出了三个结果：我们证明，只要输入的顶点数是质平方，环状 TSP 就能高效求解；我们证明，如果将{1,2}-TSP 专门用于环状实例，就能轻松高效地求解；我们还提出了一个大幅改进的近似因子，用于在双条纹环状实例上找到成本最低的欧拉连通子（多）图。

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.