An ETH-Tight Exact Algorithm for Euclidean TSP

IF 1.2 3区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

SIAM Journal on Computing Pub Date : 2023-06-05 DOI:10.1137/22m1469122

Mark de Berg, Hans L. Bodlaender, Sándor Kisfaludi-Bak, Sudeshna Kolay

引用次数: 0

Abstract

We study exact algorithms for Metric TSP in . In the early 1990s, algorithms with running time were presented for the planar case, and some years later an algorithm with running time was presented for any . Despite significant interest in subexponential exact algorithms over the past decade, there has been no progress on Metric TSP, except for a lower bound stating that the problem admits no algorithm unless ETH fails. In this paper we settle the complexity of Metric TSP, up to constant factors in the exponent and under ETH, by giving an algorithm with running time .

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Euclidean TSP的ETH-Tight精确算法

我们研究了度量TSP的精确算法。在20世纪90年代初，针对平面情况提出了具有运行时间的算法，几年后，针对任何情况提出了具有运行时间的算法。尽管在过去的十年里，人们对亚指数精确算法有了很大的兴趣，但在度量TSP上没有任何进展，除了一个下界，即除非ETH失败，否则该问题不允许算法。本文给出了一种具有运行时间的算法，解决了度量TSP的复杂度，使其在指数和ETH下达到常数因子。

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

SIAM Journal on Computing 工程技术-计算机：理论方法

CiteScore

4.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Computing aims to provide coverage of the most significant work going on in the mathematical and formal aspects of computer science and nonnumerical computing. Submissions must be clearly written and make a significant technical contribution. Topics include but are not limited to analysis and design of algorithms, algorithmic game theory, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational biology, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.