We model certain issues of future planning by introducing time parameters to the set cover problem. For example, this model captures the scenario of optimization under projections of increasing covering demand and decreasing set cost. We obtain an efficient approximation algorithm with performance guarantee independent of time, thus achieving planning for the future with the same accuracy as optimizing in the standard static model.

From a technical point of view, the difficulty in scheduling the evolution of a (set cover) solution that is “good over time” is in quantifying the intuition that “a solution which is suboptimal for time t may be chosen, if this solution reduces substantially the additional cost required to obtain a solution for t′ > t′′. We use the greedy set picking approach, however, we introduce a new criterion for evaluating the potential benefit of sets that addresses precisely the above difficulty.

The above extension of the set cover problem arose in a toolkit for automated design and architecture evolution of high speed networks. Further optimization problems that arise in the same context include survivable network design, facility location with demands and natural extensions of these problems under projections of increasing demands and decreasing costs; obtaining efficient approximation algorithms for the latter questions are interesting open problems.


Greedy Algorithm Facility Location Facility Location Problem Network Design Problem Performance Guarantee 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ball, M., Magnati, T., Monma, C., Hemhauser, G.: Handbook in Operations Research and Management Science, vol. 8. North-Holland, Amsterdam (1992)Google Scholar
  2. 2.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)zbMATHGoogle Scholar
  3. 3.
    Charikar, M., Guha, S., Tardos, E., Shmoys, D.: A constant-factor Approximation Algorithm for the k-median Problem. In: STOC Proc. (1999) (to appear)Google Scholar
  4. 4.
    Hochbaum, D.: Approximation Algorithms for NP-Hard Problems. PSW Publishing Company, Boston (1997)Google Scholar
  5. 5.
    Chvatal, V.: A Greedy Heuristic for the Set Covering Problem. Mathematics of Operations Research 4, 233–235 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Cosares, S., Deutch, D., Saniee, I., Wasem, O.: SONET Toolkit: A Decision Sup- port System for the Design of Cost-Effective Fiber Optic Networks. Interfaces 25, 20–40 (1995)CrossRefGoogle Scholar
  7. 7.
    Feige, U.: A Threshold of ln n for Approximating Set Cover. In: Proceedings of STOC 1996 (1996)Google Scholar
  8. 8.
    Goemans, M., Goldberg, A., Plotkin, S., Schmoys, D., Tardos, E., Williamson, D.: Improved Approximation Algorithms for Network Design Problems. In: Proc. SODA 1994 (1994)Google Scholar
  9. 9.
    3rd INFORMS Telecommunications Conference, Special Sessions on Network De- sign Aspects about ATM and Design and Routing for Telecommunications Net- works (May 1997)Google Scholar
  10. 10.
    Jain, K.: A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem. In: FOCS Proc. 1998 (1998)Google Scholar
  11. 11.
    Jain, K., Vazirani, V.V.: Primal-Dual Approximation Algorithms for Metric Facility Location and k-Median Problems, submitted also in,
  12. 12.
    Magnati, T., Wong, R.T.: Network Design and Transportation Planning: Models and Algorithms. Transportation Science 18, 1–55 (1984)CrossRefGoogle Scholar
  13. 13.
    Mihail, M., Shallcross, D., Dean, N., Mostrel, M.: A Commercial Application of Survivable Network Design. In: Proc. SODA 1996 (1996)Google Scholar
  14. 14.
    Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)zbMATHGoogle Scholar
  15. 15.
    Saniee, I., Bienstock, D.: ATM Network Design: Traffic Models and Optimization Based Heuristics. In: 4th INFORMS Telecommunications Conference (March 1998)Google Scholar
  16. 16.
    Williamson, D., Goemans, M., Mihail, M., Vazirani, V.: A Primal-Dual Approximation Algorithm for Generalized Steiner Network Problems. Combinatorica 15, 435–454 (1995)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Milena Mihail
    • 1
  1. 1.College of Computing and Department of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations