Minimum Latency Tours and the k-Traveling Repairmen Problem

  • Raja Jothi
  • Balaji Raghavachari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)


Given an undirected graph G=(V,E) and a source vertex s ∈ V, the k-traveling repairman (KTR) problem, also known as the minimum latency problem, asks for k tours, each starting at s and covering all the vertices (customers) such that the sum of the latencies experienced by the customers is minimum. Latency of a customer p is defined to be the distance (time) traveled before visiting p for the first time. Previous literature on the KTR problem has considered the version of the problem in which the repairtime of a customer is assumed to be zero for latency calculations. We consider a generalization of the problem in which each customer has an associated repairtime. In this paper, we present constant factor approximation algorithms for this problem and its variants.


Approximation Ratio Minimum Latency Total Latency Source Vertex Constant Factor Approximation Algorithm 
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  1. 1.
    Archer, A., Levin, A., Williamson, D.P.: Faster approximation algorithms for the minimum latency problem. In: SODA 2003 (2003)Google Scholar
  2. 2.
    Arora, S., Karakostas, G.: A 2+epsilon approximation for the k-MST problem. In: SODA 2000 (2000)Google Scholar
  3. 3.
    Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, B., Raghavan, P., Sudan, M.: The minimum latency problem. In: SODA 1994 (1994)Google Scholar
  4. 4.
    Chaudhuri, K., Godfrey, B., Rao, S., Talwar, K.: Paths, tours, and minimum latency tours. In: FOCS 2003 (2003)Google Scholar
  5. 5.
    Chekuri, C., Kumar, A.: A note on the k-traveling repairmen problem (manuscript, 2003)Google Scholar
  6. 6.
    Fakcharoenphol, J., Harrelson, C., Rao, S.: The k-traveling repairman problem. In: SODA 2003 (2003)Google Scholar
  7. 7.
    Garg, N.: A 3-approximation for the minimum tree spanning k vertices. In: FOCS 1996 (1996)Google Scholar
  8. 8.
    Goemans, M., Kleinberg, J.: An improved approximation ratio for the minimum latency problem. In: SODA 1996 (1996)Google Scholar
  9. 9.
    Gubbala, P., Pursnani, H.: Personal communication (November 2003)Google Scholar
  10. 10.
    Sahni, S., Gonzales, T.: P-complete approximation problems. JACM 23(3), 555–565 (1976)zbMATHCrossRefGoogle Scholar
  11. 11.
    Sitters, R.: The minimum latency problem is NP-hard for weighted trees. In: Cook, W.J., Schulz, A.S. (eds.) IPCO 2002. LNCS, vol. 2337, p. 230. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Raja Jothi
    • 1
  • Balaji Raghavachari
    • 1
  1. 1.Department of Computer ScienceUniversity of Texas at DallasRichardson

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