An Approximation Algorithm for the Minimum Latency Set Cover Problem

  • Refael Hassin
  • Asaf Levin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)

Abstract

The input to the minimum latency set cover problem consists of a set of jobs and a set of tools. Each job j needs a specific subset Sj of the tools in order to be processed. It is possible to install a single tool in every time unit. Once the entire subset Sj has been installed, job j can be processed instantly. The problem is to determine an order of job installations which minimizes the weighted sum of job completion times. We show that this problem is NP-hard in the strong sense and provide an e-approximation algorithm. Our approximation algorithm uses a framework of approximation algorithms which were developed for the minimum latency problem.

Keywords

Minimum sum set cover minimum latency approximation algorithm 

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References

  1. 1.
    Archer, A., Levin, A., Williamson, D.P.: Faster approximation algorithm for the minimum latency problem, Cornell OR&IE Technical report 1362 (2003)Google Scholar
  2. 2.
    Balinski, M.L.: On a selection problem. Management Science 17, 230–231 (1970)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, W., Raghavan, P., Sudan, M.: The minimum latency problem. In: Proceeding of the 26th ACM Symposium on the Theory of Computing, pp. 163–171 (1994)Google Scholar
  4. 4.
    Brucker, P.: Scheduling algorithms. Springer, Berlin (2004)MATHGoogle Scholar
  5. 5.
    Feige, U., Peleg, D., Kortsarz, G.: The dense k-subgraph Problem. Algorithmica 29, 410–421 (2001)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Feige, U., Lovász, L., Tetali, P.: Approximating min sum set cover. Algorithmica 40, 219–234 (2004)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Goemans, M.X., Kleinberg, J.: An improved approximation ratio for the minimum latency problem. Mathematical Programming 82, 111–124 (1998)MathSciNetMATHGoogle Scholar
  8. 8.
    Hall, L.A., Schulz, A.S., Shmoys, D.B., Wein, J.: Scheduling to minimize average completion time: off-line and on-line approximation algorithms. Mathematics of Operations Research 22, 513–544 (1997)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hochbaum, D.S.: Economically preferred facilities locations with networking effect (2004) (manuscript)Google Scholar
  10. 10.
    Lageweg, B.J., Lenstra, J.K., Lawler, E.L., Rinnooy Kan, A.H.G.: Computer-aided complexity classification of combinatorial problems. Communications of the ACM 25, 817–822 (1982)MATHCrossRefGoogle Scholar
  11. 11.
    Lawler, E.L.: Combinatorial Optimization: Networks and Matroids. Holt, Rinehart & Winston (1976)MATHGoogle Scholar
  12. 12.
    Lawler, E.L.: Sequencing jobs to minimize total weighted completion time subject to precedence constraints. Annals of Discrete Mathematics 2, 75–90 (1978)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Lenstra, J.K., Rinnooy Kan, A.H.G.: Complexity of scheduling under precedence constraints. Operations Research 26, 22–35 (1978)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Rhys, J.: Shared fixed cost and network flows. Management Science 17, 200–207 (1970)MATHCrossRefGoogle Scholar
  15. 15.
    Witzgall, D.D., Saunders, R.E.: Electronic mail and the locator’s dilemma. In: Ringeisen, R.D., Roberts, F.S. (eds.) Applications of Discrete Mathematics, pp. 65–84. SIAM, Philadelphia (1988)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Refael Hassin
    • 1
  • Asaf Levin
    • 2
  1. 1.Department of Statistics and Operations ResearchTel-Aviv UniversityTel-AvivIsrael
  2. 2.Department of StatisticsThe Hebrew UniversityJerusalemIsrael

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