Improved deterministic approximation algorithms for Max TSP

We present an O(n3)-time approximation algorithm for the maximum traveling salesman problem whose approximation ratio is asymptotically 61/81 where n is the number of vertices in the input complete edge-weighted (undirected) graph. We also present an O(n3)-time approximation algorithm for the metric case of the problem whose approximation ratio is asymptotically 17/20. Both algorithms improve on the previous bests.