Skip to main content
SpringerLink
Log in

Weighted independent perfect domination on cocomparability graphs

  • Conference paper
  • First Online:
Algorithms and Computation (ISAAC 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 762))

Included in the following conference series:

Abstract

Suppose G=(V,E) is a graph in which every vertex v ∃ V is associated with a cost c(v). This paper studies the weighted independent perfect domination problem on G, i.e., the problem of finding a subset D of V such that every vertex in V is equal or adjacent to exactly one vertex in D and σ{c(v): v ∃ D is minimum. We give an O(¦V∥E¦) algorithm for the problem on cocomparability graphs. The algorithm can be implemented to run in O(¦V¦2.37) time. With some modifications, the algorithm yields an O(¦V¦ + ¦E¦) algorithm on interval graphs, which are special cocomparability graphs.

Supported partly by the National Science Council of the Republic of China under grant NSC82-0208-M009-050.

DIMACS permanent member.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K. Arvind and C. Pandu Rangan, Efficient algorithms for domination problems on cocompaxability graphs, Technical Report TR-TCS-90-18 (1990), Department of Computer Science and Engineering, Indian Institute of Technology, Madras.

    Google Scholar 

  2. D. W. Bange, A. E. Barkauskas, and P. T. Slater, Efficient dominating sets in graphs, Applications of Discrete Mathematics, R. D. Ringeisen and F. S. Roberts, eds., SIAM, Philad. (1988)189–199.

    Google Scholar 

  3. A. A. Bertossi, Total domination in interval graphs, Inform. Processing Letters 23 (1986) 131–134.

    Article  Google Scholar 

  4. A. A. Bertossi, On the domatic number of interval graph, Inform. Processing Letters 28 (1988) 275–280.

    Article  Google Scholar 

  5. A. A. Bertossi and A. Gori, Total domination and irredundance in weighted interval graphs, SIAM J. Disc. Math. 1 (1988) 317–327.

    Article  Google Scholar 

  6. N. Biggs, Perfect codes in graphs, J. Comb. Theory, Series B 15 (1973) 289–296.

    Google Scholar 

  7. M. S. Chang and Y. C. Liu, Polynomial algorithms for the weighted perfect domination problems on chordal graphs and split graphs, (1993) manuscript.

    Google Scholar 

  8. M. S. Chang and Y. C. Liu, Polynomial algorithms for the weighted perfect domination problems on interval graphs, (1993) manuscript.

    Google Scholar 

  9. D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progression, Proceedings 19th Annual ACM Sysposium on Theory of Computing (1987) 1–6.

    Google Scholar 

  10. M. C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York (1980).

    Google Scholar 

  11. J. K. Keil, Total domination in interval graphs, Inform. Processing Letters 22 (1986) 171–174.

    MathSciNet  Google Scholar 

  12. D. Kratsch and L. Stewart, Domination on cocomparability graphs, (1989), preprint.

    Google Scholar 

  13. M. Livingston and Q. F. Stout, Perfect dominating sets, Congressus Numerantium 79 (1990) 187–203.

    Google Scholar 

  14. T. L. Lu, P. H. Ho and G. J. Chang, The domatic number problem in interval graphs, SIAM J. Disc. Math. 3 (1990) 531–536.

    Article  Google Scholar 

  15. G. Ramalingam and C. Pandu Rangan, Total domination in interval graphs revisited, Inform. Processing Letters 27 (1988) 17–21.

    Article  Google Scholar 

  16. G. Ramalingam and C. Pandu Rangan, A unified approach to domination problems on interval graphs, Inform. Processing Letters 27 (1988) 271–274.

    Article  Google Scholar 

  17. J. Spinrad, Transitive orientation in (n 2) time, 15th STOC Proceedings (1983) 457–466.

    Google Scholar 

  18. A. Srinivasa Rao and C. Pandu Rangan, Linear algorithm for domatic number problem on interval graphs, Inform. Processing Letters 33 (1989/90) 29–33.

    Article  Google Scholar 

  19. C. C. Yen, Algorithmic Aspects of Perfect Domination, Ph. D thesis, Institute of Information Science, National Tsing Hua University, Taiwan (1992).

    Google Scholar 

  20. C. C. Yen and R. C. T. Lee, The weighted perfect domination problem, Inform. Processing Letters 35 (1990) 295–299.

    Article  Google Scholar 

  21. C. C. Yen and R. C. T. Lee, A linear time algorithm to solve the weighted perfect domination problem in series-parallel graphs, European J. Operational Research (1992), to appear.

    Google Scholar 

  22. C. C. Yen and R. C. T. Lee, The weighted perfect domination problem and its variants, manuscript.

    Google Scholar 

Download references

Author information

Author notes

  1. Satyan R. Coorg

    Present address: Department of Applied Mathematics, National Chiao Tung University, 30050, Hsinchu, Taiwan, Republic of China

Authors and Affiliations

  1. Department of Applied Mathematics, National Chiao Tung University, 30050, Hsinchu, Taiwan, Republic of China

    Gerard J. Chang

  2. Department of Computer Science and Engineering, Indian Institute of Technology, 600 036, Madras, India

    C. Pandu Rangan & Satyan R. Coorg

Authors
  1. Gerard J. Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Pandu Rangan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Satyan R. Coorg
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

K. W. Ng P. Raghavan N. V. Balasubramanian F. Y. L. Chin

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chang, G.J., Pandu Rangan, C., Coorg, S.R. (1993). Weighted independent perfect domination on cocomparability graphs. In: Ng, K.W., Raghavan, P., Balasubramanian, N.V., Chin, F.Y.L. (eds) Algorithms and Computation. ISAAC 1993. Lecture Notes in Computer Science, vol 762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57568-5_282

Download citation

  • DOI: https://doi.org/10.1007/3-540-57568-5_282

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57568-9

  • Online ISBN: 978-3-540-48233-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation