Advertisement

Upgrading Bottleneck Constrained Forests

  • S. O. Krumke
  • M. V. Marathe
  • H. Noltemeier
  • S. S. Ravi
  • H. -C. Wirth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1517)

Abstract

We study bottleneck constrained network upgrading problems. We are given an edge weighted graph G=(V,E) where node vV can be upgraded at a cost of c(v). This upgrade reduces the delay of each link emanating from v. The goal is to find a minimum cost set of nodes to be upgraded so that the resulting network has a good performance. The performance is measured by the bottleneck weight of a constrained forest defined by a proper function [GW95]. These problems are a generalization of the node weighted constrained forest problems studied by Klein and Ravi [KR95].

The main result of the paper is a polynomial time approximation algorithm for this problem with performance guarantee of \(2 \ln (\sqrt{e}/2\cdot \vert K\vert)\), where K:={ v : f({v})=1 } is the set of terminals given by the proper function f. We also prove that the performance bound is tight up to small constant factors by providing a lower bound of ln ∣K∣. Our results are obtained by extending the elegant solution based decomposition technique of [KR95] for approximating node weighted constrained forest problems. The results presented here extend those in [KR95,KM + 97].

Keywords

Edge Weight Proper Function Performance Guarantee Steiner Tree Problem Active Cluster 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berman, O.: Improving the location of minisum facilities through network modification. Annals of Operations Research 40, 1–16 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  2. Feige, U.: A threshold of ln n for approximating set cover. In: Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (STOC 1996), pp. 314–318 (1996)Google Scholar
  3. Goemans, M.X., Goldberg, A.V., Plotkin, S., Shmoys, D.B., Tardos, E., Williamson, D.P.: Improved approximation algorithms for network design problems. In: Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 1994), January 1994, pp. 223–232 (1994)Google Scholar
  4. Goemans, M.X., Williamson, D.P.: A general approximation technique for constrained forest problems. SIAM Journal of Computing 24, 296–317 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  5. Krumke, S.O., Marathe, M.V., Noltemeier, H., Ravi, R., Ravi, S.S., Sund-aram, R., Wirth, H.C.: Improving spanning trees by upgrading nodes. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 281–291. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  6. Krumke, S.O., Noltemeier, H., Ravi, S.S., Marathe, M.V., Drang-meister, K.U.: Modifying networks to obtain low cost trees. In: D’Amore, F., Marchetti-Spaccamela, A., Franciosa, P.G. (eds.) WG 1996. LNCS, vol. 1197, pp. 293–307. Springer, Heidelberg (1997)Google Scholar
  7. Klein, P., Ravi, R.: A nearly best-possible approximation for node-weighted Steiner trees. Journal of Algorithms 19, 104–115 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  8. Phillips, C.: The network inhibition problem. In: Proceedings of the 25th Annual ACM Symposium on the Theory of Computing (STOC 1993), May 1993, pp. 288–293 (1993)Google Scholar
  9. Paik, D., Sahni, S.: Network upgrading problems. Networks 26, 45–58 (1995)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • S. O. Krumke
    • 1
  • M. V. Marathe
    • 2
  • H. Noltemeier
    • 3
  • S. S. Ravi
    • 4
  • H. -C. Wirth
    • 3
  1. 1.Department OptimizationKonrad-Zuse-Zentrum für Informationstechnik BerlinBerlin-DahlemGermany
  2. 2.Los Alamos National LaboratoryLos AlamosUSA
  3. 3.Department of Computer ScienceUniversity of WürzburgWürzburgGermany
  4. 4.Department of Computer ScienceUniversity at Albany – SUNYAlbanyUSA

Personalised recommendations