A Work-Optimal Coarse-Grained PRAM Algorithm for Lexicographically First Maximal Independent Set

  • Jens Gustedt
  • Jan Arne Telle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2841)


The Lexicographically First Maximal Independent Set Problem on graphs with bounded degree 3 is at most \(\sqrt{n}\)-complete, and thus very likely not parallelizable in a fine-grained setting. On the other hand, we show that in a coarse-grained setting (few processors and a lot of data) the situation is different, by giving a work-optimal algorithm on a shared memory machine for n and p such that p ·log p  ∈ O(log n).


Parallel Algorithm Lookup Table Input Graph Block Versus Block Graph 
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  1. 1.
    Brent, R.P.: The parallel evaluation of generic arithmetic expressions. Journal of the ACM 21(2), 201–206 (1974)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Condon, A.: A theory of strict P-completeness. Computational Complexity 4, 220–241 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Culler, D., Karp, R., Patterson, D., Sahay, A., Schauser, K., Santos, E., Subramonian, R., Von Eicken, T.: LogP: Towards a Realistic Model of Parallel Computation. In: Proceeding of 4th ACMSIGPLAN Symp. on Principles and Practises of Parallel Programming, pp. 1–12 (1993)Google Scholar
  4. 4.
    Dehne, F., Fabri, A., And Rau-Chaplin, A.: Scalable parallel computational geometry for coarse grained multicomputers. International Journal on Computational Geometry 6(3), 379–400 (1996)zbMATHCrossRefGoogle Scholar
  5. 5.
    Ferreira, A., And Schabanel, N.: A randomized BSP/CGMalgorithm for the maximal independent set. Parallel Processing Letters 9(3), 411–422 (2000)CrossRefGoogle Scholar
  6. 6.
    Gebremedhin, A.H., Guérin Lassous, I., Gustedt, J., Telle, J.: Graph coloring on a coarse grained multiprocessor. In: Brandes, U., Wagner, D. (eds.) WG 2000. LNCS, vol. 1928, pp. 184–195. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Gebremedhin, A.H., Guérin Lassous, I., Gustedt, J., Telle, J.: PRO: a model for parallel resource-optimal computation. In: 16th Annual International Symposiumon High Performance Computing Systems and Applications, The Institute of Electrical and Electronics Engineers, pp. 106–113. IEEE, Los Alamitos (2002)Google Scholar
  8. 8.
    Greenlaw, R., Hoover, J., Ruzzo, W.: Limits to parallel computation: Pcompleteness theory. Oxford University Press, Oxford (1995)Google Scholar
  9. 9.
    Karp, R.M., Ramachandran, V.: Parallel Algorithms for Shared-Memory Machines. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. Algorithms and Complexity, vol. A, pp. 869–941. Elsevier Science Publishers B.V., Amsterdam (1990)Google Scholar
  10. 10.
    Kruskal, C.P., Rudolph, L., Snir, M.: A complexity theory of efficient parallel algorithms. Theoretical Computer Science 71(1), 95–132 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Miyano, S.: The lexicographically first maximal subgraph problems: P-completeness and NC-algorithms. Mathematical Systems Theory 22(1), 47–73 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Uehara, R.: A measure for the lexicographically first maximal independent set problem and its limits. International Journal of Foundations of Computer Science 10(4), 473–482 (1999)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Valiant, L.G.: A bridging model for parallel computation. Communications of the ACM 33(8), 103–111 (1990)CrossRefGoogle Scholar
  14. 14.
    Vitter, J.S., Simons, R.A.: New classes for parallel comlexity. IEEE Trans. Comput. 35, 403–418 (1986)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jens Gustedt
    • 1
  • Jan Arne Telle
    • 2
  1. 1.LORIA & INRIA LorraineFrance
  2. 2.University of BergenBergenNorway

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