Approximation Algorithms for Not Necessarily Disjoint Clustered TSP Nili Guttmann-Beck, Eyal Knaan, and Michal Stern Vol. 22, no. 4, pp. 555-575, 2018. Regular paper. Abstract Let $G=(V,E)$ be a complete undirected graph with vertex set $V$, edge set $E$ and let $H = \langle G,\mathcal{S} \rangle$ be a hypergraph, where $\mathcal{S}$ is a set of not necessarily disjoint clusters $S_1,\ldots,S_m$, $S_i \subseteq V$ $\forall i \in \{ 1,\ldots,m \}$. 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. Submitted: June 2017. Reviewed: June 2018. Revised: September 2018. Accepted: September 2018. Final: September 2018. Published: September 2018. Communicated by Susanne Albers article (PDF) BibTeX