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

TL;DR

This paper introduces a fast combinatorial 4/5-approximation algorithm for the maximum traveling salesman problem, improving the previous best approximation ratio from 7/9 using novel graph elimination and edge exchange techniques.

Contribution

The paper presents a new 4/5-approximation algorithm for Max TSP, employing innovative methods like half-edges, edge coloring, and edge exchanging to enhance approximation quality.

Findings

Achieves a 4/5 approximation ratio for Max TSP

Introduces novel techniques of half-edges and edge coloring

Improves upon the previous 7/9 approximation bound

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 $v$".