Dynamic Storage Allocation and On-Line Colouring Interval Graphs

  • N. S. Narayanaswamy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3106)

Abstract

We present an improved on-line algorithm for colouring interval graphs with bandwidth. This problem has recently been studied in [1] and a 195-competitive online strategy has been presented. We improve this by presenting a 10-competitive strategy. To achieve this result, we use the online colouring algorithm presented in [8,9]. We also present a new analysis of a polynomial time 3-approximation algorithm for Dynamic Storage Allocation(DSA) using features of the optimal on-line algorithm for colouring interval graphs [8,9].

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adamy, U., Erlebach, T.: Online coloring of intervals with bandwidth. In: Proceedings of the First Workshop on Approximation and Online Algorithms (2003)Google Scholar
  2. 2.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)MATHGoogle Scholar
  3. 3.
    Feldmann, A., Maggs, B., Sgall, J., Sleator, D.D., Tomkins, A.: Competitive analysis of call admission algorithms that allow delay. Technical Report CMU-CS- 95-102, Carnegie Mellon University (1995)Google Scholar
  4. 4.
    Garey, M.R., Johnson, D.S.: Computers and Intractability - A Guide to the Theory of NP-Completeness. Freeman, New York (1979)MATHGoogle Scholar
  5. 5.
    Gergov, J.: Approximation algorithms for dynamic storage allocation. In: Díaz, J. (ed.) ESA 1996. LNCS, vol. 1136, pp. 52–61. Springer, Heidelberg (1996)Google Scholar
  6. 6.
    Gergov, J.: Algorithms for compile-time memory optimization. In: Proc. of 10th ACM-SIAM Symposium on Discrete Algorithms, pp. 907–908 (1999)Google Scholar
  7. 7.
    Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, London (1980)MATHGoogle Scholar
  8. 8.
    Kierstead, H.A.: A polynomial approximation algorithm for dynamic storage allocation. Discrete Mathematics 88, 231–237 (1991)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kierstead, H.A., Trotter, W.T.: An extremal problem in recursive combinatorics. Congressus Numeratium 33, 143–153 (1981)MathSciNetGoogle Scholar
  10. 10.
    Knuth, D.E.: Art of Computer Programming. Fundamental Algorithms, vol. 1. Addison-Wesley, Reading (1973)Google Scholar
  11. 11.
    Leonardi, S., Marchetti-Spaccamela, A., Vitaletti, A.: Approximation algorithms for bandwidth and storage allocation problems under real time constraints. In: Kapoor, S., Prasad, S. (eds.) FST TCS 2000. LNCS, vol. 1974, pp. 409–420. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  12. 12.
    Slusarek, M.: A colouring algorithm for interval graphs. In: Kreczmar, A., Mirkowska, G. (eds.) MFCS 1989. LNCS, vol. 379, pp. 471–480. Springer, Heidelberg (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • N. S. Narayanaswamy
    • 1
  1. 1.Department of Computer Science and EngineeringIIT-MadrasChennaiIndia

Personalised recommendations