The TSP-approach to approximate solving the m-Cycles Cover Problem

In the m-Cycles Cover problem it is required to find a collection of m vertex-disjoint cycles that covers all vertices of the graph and the total weight of edges in the cover is minimum (or maximum). The problem is a generalization of the Traveling salesmen problem. It is strongly NP-hard. We discuss a TSP-approach that gives polynomial approximate solutions for this problem. It transforms an approximation TSP algorithm into an approximation m-CCP algorithm. In this paper we present a number of successful transformations with proven performance guarantees for the obtained solutions.