Approximation Algorithms for Not Necessarily Disjoint Clustered TSP - Guttmann-Beck, Nili; Knaan, Eyal; Stern, Michal (Journal of Graph Algorithms and Applications, 2018)
Let G=(V,E) be a complete undirected graph with vertex set V, edge set E and let H = G,S be a hypergraph, where S is a set of not necessarily disjoint clusters S_1,…,S_m, S_i V i { 1,…,m }. The clustered traveling salesman problem CTSP is to compute a shortest Hamiltonian path that visits each one of the vertices once, such that the vertices of each cluster are visited consecutively. In this paper, we present a 4-approximation algorithm for the general case. When the intersection graph is a path, we present a 5/3-approximation algorithm. When the clusters' sizes are all bounded by a constant and the intersection graph is connected, we present an optimal polynomial time algorithm.