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

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

We design a polynomial time 8/7-approximation algorithm for the Traveling Salesman Problem in which all distances are either one or two. This improves over the best known approximation factor of 7/6 for that problem. As a direct application we get a 7/6-approximation algorithm for the Maximum Path Cover Problem, similarily improving upon the best known approximation factor for that problem. The result depends on a new method of consecutive path cover improvements and on a new analysis of certain related color alternating paths. This method could be of independent
interest.