10.05.2006

We design a polynomial time 8/7-approximation algorithm for theTraveling Salesman Problem in which all distances areeither one or two. This improves over the best known approximationfactor for that problem. As a direct application we get a7/6-approximation algorithm for the Maximum Path Cover Problem,similarly improving upon the best known approximation factorfor that problem. The result depends on a new method of consecutivepath cover improvements and on a new analysis of certain related coloralternating paths. This method could be of independent interest.