THE APPROXIMATION RATIO OF THE k-OPT HEURISTIC FOR THE EUCLIDEAN TRAVELING SALESMAN PROBLEM

被引：5

作者：

Brodowsky, Ulrich A.

Hougardy, Stefan ^{[1
,2
]}

Zhong, Xianghui ^{[1
,2
]}

机构：

[1] Univ Bonn, Res Inst Discrete Math, D-53113 Bonn, Germany

[2] Univ Bonn, Hausdorff Ctr Math, D-53113 Bonn, Germany

来源：

SIAM JOURNAL ON COMPUTING | 2023年 / 52卷 / 04期

关键词：

traveling salesman problem; Euclidean TSP; approximation algorithm; k-Opt heuristic; ALGORITHM;

D O I：

10.1137/21M146199X

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The k-Opt heuristic is a simple improvement heuristic for the traveling salesman prob-lem. It starts with an arbitrary tour and then repeatedly replaces k edges of the tour by k other edges, as long as this yields a shorter tour. We will prove that for the 2-dimensional Euclidean traveling salesman problem with n cities the approximation ratio of the k-Opt heuristic is theta(log n/ log log n). This improves the upper bound of O(log n) given by Chandra, Karloff, and Tovey in [SIAM J. Com-put., 28 (1999), pp. 1998--2029] and provides for the first time a nontrivial lower bound for the case k >= 3. Our results not only hold for the Euclidean norm but extend to arbitrary p-norms with 1 <= p < infinity .

引用

页码：841 / 864

页数：24

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