A 4/5-Approximation Algorithm For The Maximum Traveling Salesman Problem

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 4/5 - approximation algorithm for Max TSP. The previous best approximation for this problem was 7/9. The new algorithm is based on a technique of eliminating difficult subgraphs via gadgets with half-edges, a new method of edge coloring and a technique of exchanging edges.