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Approximation Algorithms with Bounded Performance Guarantees for the Clustered Traveling Salesman Problem

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Abstract.

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 Vis partitioned into clusters V 1 , . . ., V k . The clustered traveling salesman problemis 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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Authors and Affiliations

  1. Department of Statistics and Operations Research, Tel-Aviv University, 69978, Tel-Aviv, Israel

    N. Guttmann-Beck & R. Hassin

  2. Department of Computer Science and UMIACS, University of Maryland, 20742, College Park, MD, USA

    S. Khuller

  3. Department of Computer Science, The University of Texas at Dallas, 75083-0688, Richardson, TX, US

    B. Raghavachari

Authors
  1. N. Guttmann-Beck
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  2. R. Hassin
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  3. S. Khuller
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  4. B. Raghavachari
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Additional information

Received February 13, 1998; revised July 8, 1998.

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Guttmann-Beck, N., Hassin, R., Khuller, S. et al. Approximation Algorithms with Bounded Performance Guarantees for the Clustered Traveling Salesman Problem. Algorithmica 28, 422–437 (2000). https://doi.org/10.1007/s004530010045

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  • DOI: https://doi.org/10.1007/s004530010045

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