IMPROVING APPROXIMATION RATIOS FOR THE CLUSTERED TRAVELING SALESMAN PROBLEM

The clustered traveling salesman problem (CTSP) is a generalization of the traveling salesman problem (TSP) in which the set of cities is divided into clusters and the salesman must consecutively visit the cities of each cluster. It is well known that TSP is NP-hard, and hence CTSP is NP-hard as well. Guttmann-Beck et al. (2000) designed approximation algorithms for several variants of CTSP by decomposing it into subproblems including the traveling salesman path problem (TSPP). In this paper, we improve approximation ratios by applying a recent improved approximation algorithm for TSPP by Zenklusen (2019).