Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Algorithms

SIGAL 1990: Algorithms pp 388–396Cite as

A heuristic algorithm for the k-center problem with vertex weight

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 450))

Abstract

In this paper, the NP-hard k-center problem with vertex weight is investigated. The problem is to choose k vertices as service centers so that the maximum weighted service delivery distance to any vertex is minimized. The notions of a neighbor vertex set and a d-restricted digraph based on weighted distance are introduced. The proposed algorithm uses a greedy strategy to choose the vertex with maximum vertex weight as the next service vertex. We have proved that the proposed algorithm generates results that are guaranteed to be no greater than twice the optimal solution values. This is the best possible polynomial time heuristic unless P=NP.

This research is based in part upon work supported by the Texas Advanced Research Program under grant 1028-ARP.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

6. References

  1. T. Feder and D. H. Greene, Optimal Algorithms for Approximate Clustering, ACM Symposium on Theory of Computing, 1988, pp. 434–444.

    Google Scholar 

  2. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.

    Google Scholar 

  3. T. F. González, Clustering to Minimize the Maximum Intercluster Distance, Theoretical Computer Science, Vol. 38, 1985, pp. 293–306.

    Google Scholar 

  4. G. Y. Handler and P. B. Mirchandani, Location on Networks: Theory and Algorithms, MIT Press, Cambridge, MA, 1979.

    Google Scholar 

  5. D. S. Hochbaum and D. B. Shmoys, A Unified Approach to Approximation Algorithms for Bottleneck Problems, Journal of ACM, Vol. 33, 1986, pp. 533–550.

    Google Scholar 

  6. O. Kariv and S. L. Hakimi, An Algorithmic Approach to Network Location Problems. Part I: The p-Centers, SIAM Journal of Appl. Math., Vol. 37, 1979, pp. 513–538.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, University of Houston, 77204-3475, Houston, Texas, USA

    Qingzhou Wang & Kam Hoi Cheng

Authors
  1. Qingzhou Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kam Hoi Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Tetsuo Asano Toshihide Ibaraki Hiroshi Imai Takao Nishizeki

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, Q., Cheng, K.H. (1990). A heuristic algorithm for the k-center problem with vertex weight. In: Asano, T., Ibaraki, T., Imai, H., Nishizeki, T. (eds) Algorithms. SIGAL 1990. Lecture Notes in Computer Science, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52921-7_88

Download citation

  • DOI: https://doi.org/10.1007/3-540-52921-7_88

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52921-7

  • Online ISBN: 978-3-540-47177-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation