D S ] 31 D ec 2 01 5 A 4 / 5-Approximation Algorithm for the Maximum Traveling Salesman Problem ∗

In the maximum traveling salesman problem (Max TSP) we are gi v n 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 4 5 approximation algorithm for Max TSP. The previous best approximation for this problem was 7 9 . The new algorithm is based on a novel technique of eliminati ng difficult subgraphs viahalf-edges , a new method of edge coloring and a technique of exchanging e dges. A half-edgeof edgee = (u, v) is informally speaking “a half of e containing eitheru or v”. Partly supported by Polish National Science Center grant UM O-2013/11/B/ST6/01748 szymon.dudycz@gmail.com jasiekmarc@stud.cs.uni.wroc.pl abraka@cs.uni.wroc.pl rybicki.bartek@gmail.com