An extension of the Christofides heuristic for the generalized multiple depot multiple traveling salesmen problem

We study a generalization of the classical traveling salesman problem, where multiple salesmen are positioned at different depots, of which only a limited number (k) can be selected to service customers. For this problem, only two 2-approximation algorithms are available in the literature. Here, we improve on these algorithms by showing that a non-trivial extension of the well-known Christofides heuristic has a tight approximation ratio of 2−1/(2k). In doing so, we develop a body of analysis which can be used to build new approximation algorithms for other vehicle routing problems.