Skip to main content
SpringerLink
Log in

Deferred-query—An efficient approach for problems on interval and circular-arc graphs

Extended abstract

  • Conference paper
  • First Online:
Algorithms and Data Structures (WADS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 709))

Included in the following conference series:

Abstract

An efficient approach, called deferred-query, is proposed in this paper to design O(n) algorithms for the domatic partition, optimal path cover, Hamiltonian path, Hamiltonian circuit and matching problems on a set of sorted intervals. Using above results, the optimal path cover, hamiltonian path and hamiltonian circuit problems can also be solved in O(n) time on a set of sorted arcs.

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. S. Rao Arikati and C. Pandu Rangan, Linear algorithm for optimal path cover problem on interval graphs, Inform. Process. Lett. 35 (1990), 149–153.

    Google Scholar 

  2. A. A. Bertossi, On the domatic number of interval graphs, Inform. Process. Lett. 28 (1988) 275–280.

    Google Scholar 

  3. A. A. Bertossi, The edge Hamiltonian path problem is NP-complete, Inform. Process. Lett. 13 (1981) 157–159.

    Article  Google Scholar 

  4. A. A. Bertossi and M. A. Bonuccelli, Hamiltonian Circuits in Interval Graph Generalizations, Information Process. Lett. 23 (1986) 195–200.

    Google Scholar 

  5. M. A. Bonuccelli and D. P. Bovet, Minimum Node Disjoint Path Covering for Circular-Arc Graphs, Information Process. Lett. 8 (1979) 159–161.

    Article  Google Scholar 

  6. K. S. Booth and G. S. Leuker, Testing for consecutive ones property, interval graphs and graph planarity using PQ-tree algorithms, J. Comput. system Sci. 13 (1976), 335–379.

    Google Scholar 

  7. M. S Chang, O(n) Algorithms for the Hamiltonian Cycle and Node Disjoint Path Cover Problems on Circular-Arc Graphs, Preprint.

    Google Scholar 

  8. E. J. Cockayne and S. T. Hedetniemi, Towards a theory of domination in graphs, Networks 7 (1977), 247–261.

    Google Scholar 

  9. M. S. Chang, S. L. Peng and J. L. Liaw, Deferred-Query, An Efficient Approach for Some Problems on Interval Graphs, Preprint.

    Google Scholar 

  10. M. Farber, Domination, independent domination, and duality in strongly chordal graphs, Disc. Appl. Math. 7 (1984), 115–130.

    Article  Google Scholar 

  11. H. N. Gabow and R. E. Tarjan, A linear-time algorithm for a special case of disjoint set union, J. Comput. System Sci. 30 (1985), 209–221.

    Article  Google Scholar 

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

    Google Scholar 

  13. M. R. Garey, D. S. Johnson and R. E. Tarjan, The planar Hamiltonian circuit problem is NP-complete, SIAM J. Comput. 5 (1976), 704–714.

    Article  Google Scholar 

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

    Google Scholar 

  15. M. C. Golumbic and P. L. Hammer, Stability in Circular-Arc Graphs, J. of Algorithms 9 (1988) 314–320.

    Google Scholar 

  16. W. L. Hsu, W. K. Shih and T. C. Chern, An O(n 2logn) Time Algorithm for the Hamiltonian Cycle Problem, SIAM J. on Compt.

    Google Scholar 

  17. W. L. Hsu and K. H. Tsai, Linear Time Algorithms on Circular-Arc Graphs, Information Process. Lett. 40 (1991) 123–129.

    Google Scholar 

  18. D. S. Johnson, The NP-Complete Column: an Ongoing Guide, J. of Algorithms 6 (1985) 434–451.

    Google Scholar 

  19. J. M. Keil, Finding Hamiltonian Circuits in Interval Graphs, Inform. Process. Lett. 20 (1985), 201–206.

    Google Scholar 

  20. M. S. Krishnamoorthy, An NP-hard problem in a bipartite graphs, SIGACT News 7 (1), (1976) 26.

    Google Scholar 

  21. 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.

    Google Scholar 

  22. G. K. Manacher and T. A. Mankus, Determining the domatic number and a domatic partition of an interval graph in time O(n) given its sorted model, Technique report, Submitted to SIAM J. Disc. Math. 1991.

    Google Scholar 

  23. G. K. Manacher, T. A. Mankus and C. J. Smith, An Optimum O(nlogn) Algorithm for Finding a Canonical Hamiltonian Path and a Canonical Hamiltonian circuit in a set of intervals, Inform. Process. Lett. 35 (1990), 205–211.

    MathSciNet  Google Scholar 

  24. S. Masuda and K. Nakajima, An Optimal Algorithm for Finding a Maximum Independent Set of a Circular-Arc Graph, SIAM J. Comput. 17 (1988) 41–52.

    Article  Google Scholar 

  25. A. Moitra and R. C. Johnson, A parallel algorithm for maximum matching on interval graphs, 1989 International Conference on Parallel Processing, III 114–120.

    Google Scholar 

  26. S. L. Peng and M. S. Chang, A new approach for domatic number problem on interval graphs, Proceedings of National Computer Symposium 1991 R.O.C., 236–241.

    Google Scholar 

  27. F. S. Roberts, Graph theory and its Applications to problems of society, SIAM, Philadelphia, PA, 1978.

    Google Scholar 

  28. A. Srinivasa Rao and C. Pandu Rangan, Linear algorithm for domatic number problem on interval graphs, Inform. Process. Lett. 33 (1989), 29–33.

    Google Scholar 

  29. A. Tucker, An Efficient Test for Circular-Arc Graphs, SIAM J. Comput. 9 (1980) 1–24.

    Article  Google Scholar 

  30. P. Van Emde Boas, Preserving order in a forest in less than logarithmic time and linear space, Inform. Process. Lett. 6 (1977), 80–82.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Shiun, Chiayi, Taiwan 621

    Maw-Shang Chang, Sheng-Lung Peng & Jenn-Liang Liaw

Authors
  1. Maw-Shang Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sheng-Lung Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jenn-Liang Liaw
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Frank Dehne Jörg-Rüdiger Sack Nicola Santoro Sue Whitesides

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chang, MS., Peng, SL., Liaw, JL. (1993). Deferred-query—An efficient approach for problems on interval and circular-arc graphs. In: Dehne, F., Sack, JR., Santoro, N., Whitesides, S. (eds) Algorithms and Data Structures. WADS 1993. Lecture Notes in Computer Science, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57155-8_250

Download citation

  • DOI: https://doi.org/10.1007/3-540-57155-8_250

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57155-1

  • Online ISBN: 978-3-540-47918-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation