A Simpler Linear-Time Recognition of Circular-Arc Graphs

  • Haim Kaplan
  • Yahav Nussbaum
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4059)


We give a linear time recognition algorithm for circular-arc graphs. Our algorithm is much simpler than the linear time recognition algorithm of McConnell [10] (which is the only linear time recognition algorithm previously known). Our algorithm is a new and careful implementation of the algorithm of Eschen and Spinrad [4, 5]. We also tighten the analysis of Eschen and Spinrad.


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  1. 1.
    Booth, K.S., Lueker, G.S.: Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. J. Comput. Syst. Sci. 13(3), 335–379 (1976)MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Conitzer, V., Derryberry, J., Sandholm, T.: Combinatorial auctions with structured item graphs. In: Proceedings of the Nineteenth National Conference on Artificial Intelligence, pp. 212–218 (2004)Google Scholar
  3. 3.
    Deng, X., Hell, P., Huang, J.: Linear-time representation algorithms for proper circular-arc graphs and proper interval graphs. SIAM J. Comput. 25(2), 390–403 (1996)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Eschen, E.M.: Circular-arc graph recognition and related problems. PhD thesis, Department of Computer Science, Vanderbilt University (1997)Google Scholar
  5. 5.
    Eschen, E.M., Spinrad, J.P.: An O(n 2) algorithm for circular-arc graph recognition. In: SODA 1993: Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 128–137 (1993)Google Scholar
  6. 6.
    Hsu, W.-L.: O(mn) algorithms for the recognition and isomorphism problems on circular-arc graphs. SIAM J. Comput. 24(3), 411–439 (1995)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hsu, W.-L., McConnell, R.M.: PC-trees and circular-ones arrangements. Theor. Comput. Sci. 296(1), 99–116 (2003)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Lin, M.C., Szwarcfiter, J.L.: Efficient construction of unit circular-arc models. In: SODA 2006: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, pp. 309–315 (2006)Google Scholar
  9. 9.
    Ma, T.-H., Spinrad, J.P.: Avoiding matrix multiplication. In: Möhring, R.H. (ed.) WG 1990. LNCS, vol. 484, pp. 61–71. Springer, Heidelberg (1991)Google Scholar
  10. 10.
    McConnell, R.M.: Linear-time recognition of circular-arc graphs. Algorithmica 37(2), 93–147 (2003)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    McConnell, R.M., Spinrad, J.P.: Modular decomposition and transitive orientation. Discrete Mathematics 201(1-3), 189–241 (1999)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Spinrad, J.P.: Circular-arc graphs with clique cover number two. Journal of Combinatorial Theory Series B 44(3), 300–306 (1988)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Spinrad, J.P.: Efficient Graph Representations. Fields Institute Monographs, vol. 19. American Mathematical Society (2003)Google Scholar
  14. 14.
    Spinrad, J.P., Valdes, J.: Recognition and isomorphism of two dimensional partial orders. In: Díaz, J. (ed.) ICALP 1983. LNCS, vol. 154, pp. 676–686. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  15. 15.
    Stefanakos, S., Erlebach, T.: Routing in all-optical ring networks revisited. In: Proceedings of the 9th IEEE Symposium on Computers and Communication, pp. 288–293 (2004)Google Scholar
  16. 16.
    Tucker, A.C.: An efficient test for circular-arc graphs. SIAM J. Comput. 9(1), 1–24 (1980)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Haim Kaplan
    • 1
  • Yahav Nussbaum
    • 1
  1. 1.School of Computer ScienceTel Aviv UniversityTel AvivIsrael

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