Approximation Algorithms with Bounded Performance Guarantees for the Clustered Traveling Salesman Problem
Let G=(V,E) be a complete undirected graph with vertex set V, edge set E, and edge weights l(e) satisfying triangle inequality. The vertex set V is partitioned into clustersV 1, ..., V k . The clustered traveling salesman problem (CTSP) is to compute a shortest Hamiltonian cycle (tour) that visits all the vertices, and in which the vertices of each cluster are visited consecutively. Since this problem is a generalization of the traveling salesman problem, it is NP-hard. In this paper, we consider several variants of this basic problem and provide polynomial time approximation algorithms for them.
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