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arXiv · 1512.09236

A $4/5$ - Approximation Algorithm for the Maximum Traveling Salesman Problem

Szymon Dudycz·Jan Marcinkowski·Katarzyna Paluch·Bartosz Rybicki
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Abstract

In the maximum traveling salesman problem (Max TSP) we are given a complete undirected graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum weight. We present a fast combinatorial $\frac 45$ - approximation algorithm for Max TSP. The previous best approximation for this problem was $\frac 79$. The new algorithm is based on a novel technique of eliminating difficult subgraphs via half-edges, a new method of edge coloring and a technique of exchanging edges. A half-edge of edge $e=(u,v)$ is informally speaking "a half of $e$ containing either $u$ or $v$".

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Szymon Dudycz, Jan Marcinkowski, Katarzyna Paluch, Bartosz Rybicki. 2016-03-20. A $4/5$ - Approximation Algorithm for the Maximum Traveling Salesman Problem. https://arxiv.org/abs/1512.09236

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