A 1.5-Approximation for Symmetric Euclidean Open Loop TSP

IF 3.4 3区计算机科学 Q2 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Access Pub Date : 2024-10-02 DOI:10.1109/ACCESS.2024.3472282

Alok Chauhan

引用次数: 0

Abstract

Travelling Salesman Problem (TSP) is NP-hard and therefore lacks efficient algorithm that provides optimal solution. So far, a benchmark in this area is Christofides’ Algorithm, which provides an upper bound of 3/2 for metric TSP. In this paper, it is shown that a simple nearest neighbor heuristic called 2- Repetitive Nearest Neighbor (2-RNN) with much simpler implementation without the need to construct minimum spanning tree and Euler tour also has the approximation ratio of 3/2 for open loop symmetric Euclidean TSP which also matches with current standard for open loop TSP. Experiments also show that the average performance of 2-RNN in terms of gap percentage (18.75) is better than that of Christofides’ algorithm (28.09) for eight instances of TSPLIB dataset and gap percentage of 1.06 (2-RNN) and 9.10 (Christofides) for 6449 instances of the Dots dataset, albeit at the cost of an order of magnitude higher time complexity.

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对称欧几里得开环 TSP 的 1.5 近似值

旅行推销员问题（Travelling Salesman Problem，TSP）是一个 NP 难问题，因此缺乏能提供最优解的高效算法。迄今为止，该领域的基准算法是 Christofides 算法，它为公制 TSP 提供了 3/2 的上限。本文表明，一种名为 2- Repetitive Nearest Neighbor (2-RNN) 的简单近邻启发式算法无需构建最小生成树和欧拉游，其实现简单得多，而且对开环对称欧氏 TSP 的近似率也达到了 3/2，这也符合当前开环 TSP 的标准。实验还表明，在 TSPLIB 数据集的 8 个实例中，2-RNN 在差距百分比（18.75）方面的平均性能优于 Christofides 算法（28.09）；在 Dots 数据集的 6449 个实例中，2-RNN 和 Christofides 的差距百分比分别为 1.06（2-RNN）和 9.10（Christofides），尽管其代价是时间复杂度高出一个数量级。

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

IEEE Access COMPUTER SCIENCE, INFORMATION SYSTEMSENGIN-ENGINEERING, ELECTRICAL & ELECTRONIC

CiteScore

9.80

自引率

7.70%

发文量

6673

审稿时长

6 weeks

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