Skip to main content
SpringerLink
Log in

Efficient parallel graph coloring with prioritization

  • Irregular Data Structures and Applications
  • Conference paper
  • First Online:
Parallel Symbolic Languages and Systems (PSLS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1068))

Included in the following conference series:

Abstract

Graph coloring is an interesting problem that is intuitive and simple to formulate, yet difficult to solve efficiently. The applications of graph coloring are numerous, ranging from scheduling to solving linear systems. Because graph coloring is computationally intensive, a parallel algorithm is desirable. In this paper, we present a set of parallel graph coloring heuristics and describe their implementation in an environment supporting machine-independent parallel programming. The heuristics are intended to provide consistent, monotonically increasing speedups as the number of processors is increased. We present some performance results that demonstrate the effectiveness of our heuristics and the utility of our approach.

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. D. Brélaz. New methods to color the vertices of a graph. Communications of the ACM, 22:251–256, 1979.

    Google Scholar 

  2. Preston Briggs, Keith D. Cooper, and Linda Torczon. Improvements to graph coloring register allocation. ACM Transactions on Programming Languages and Systems, 16(3):428–455, May 1994.

    Google Scholar 

  3. M. Chams, A. Hertz, and D. de Werra. Some experiments with simulated annealing for coloring graphs. European Journal of Operational Research, Vol. 32,:, pages 260–266, 1987.

    Google Scholar 

  4. T.F. Coleman and J.J. Moré. Estimation of sparse Jacobian matrices and graph coloring problems. SIAM Journal on Numerical Analysis, 20:187–209, 1983.

    Google Scholar 

  5. M.R. Garey and D.S. Johnson. Computers and Intractability. W.H. Freeman, New York, 1979.

    Google Scholar 

  6. R. Halstead. Parallel symbolic computing. IEEE Computer, pages 35–43, August 1986.

    Google Scholar 

  7. A. Hertz and D. de Werra. Using tabu search techniques for graph coloring. Computing, Vol. 39,:, pages 345–351, 1987.

    Google Scholar 

  8. Mark T. Jones and Paul E. Plassmann. A parallel graph coloring heuristic. SIAM J. Sci. Statist. Comput., 14(3):654–669, May 1993.

    Google Scholar 

  9. M.T. Jones and P.E. Plassmann. Scalable iterative solution of sparse linear systems. Parallel Computing, 20:753–773, 1994.

    Google Scholar 

  10. R.K. Gjertsen Jr. Parallel graph coloring heuristics. Technical report, University of Illinois at Urbana-Champaign, 1994. Master's Thesis, Dept. of Computer Sceince.

    Google Scholar 

  11. L. V. Kale. The Chare Kernel parallel programming language and system. In Proceedings of the International Conference on Parallel Processing, volume II, pages 17–25, 1990.

    Google Scholar 

  12. L.V. Kale. Parallel problem solving. In Vipin Kumar, P. S. Gopolakrishnan, and L. N. Kanal, editors, Parallel Algorithms for Machine Intelligence and Vision, pages 146–181. Springer-Verlag, 1989.

    Google Scholar 

  13. L.V. Kale, B. Ramkumar, V. Saletore, and A.B. Sinha. Prioritization in parallel symbolic computing. Lecture Notes in Computer Science, 748:12–41, 1993.

    Google Scholar 

  14. G. J. Li and B.W. Wah. Coping with anomalies in parallel branch-and-bound algorithms. In IEEE Transactions on Computers, pages 568–573, June 1986.

    Google Scholar 

  15. R.G. Melhem and V.S. Ramarao. Multicolor reorderings of sparse matrices resulting from irregular grids. ACM Transactions on Mathematical Software, 14:117–138, 1988.

    Google Scholar 

  16. O. Ore. The Four-Color Problem. Academic Press, New York, 1967.

    Google Scholar 

  17. J.M. Ortega. Orderings for conjugate gradient preconditionings. SIAM Journal on Optimization, 1:565–582, 1991.

    Google Scholar 

  18. C. Pommerell, M. Annaratone, and W. Fichtner. A set of new mapping and coloring heuristics for distributed-memory parallel processors. SIAM Journal on Scientific and Statistical Computing, 13:194–226, 1992.

    Google Scholar 

  19. B. Richards. Parallel graph coloring with Charm. Technical report, University of Illinois at Urbana-Champaign, 1994. Master's Thesis, Dept. of Computer Science.

    Google Scholar 

  20. V. Saletore and L.V. Kale. Consistent linear speedups for a first solution in parallel state-space search. In Proceedings of the AAAI, pages 227–233, August 1990.

    Google Scholar 

  21. V.A. Saletore. Machine independent parallel execution of speculative computations. Technical report, University of Illinois, Urbana, Illinois, 1990. PhD Thesis, Dept. of Computer Sceince.

    Google Scholar 

  22. A. Sinha, L.V. Kale, and B. Ramkumar. A dynamic and adaptive quiescence detection algorithm. Technical Report 93-11, Parallel Programming Laboratory, Department of Computer Science, University of Illinois, 1993.

    Google Scholar 

  23. Amitabh Sinha and L.V. Kale. A load balancing strategy for prioritized execution of tasks. In Seventh International Parallel Processing Symposium, pages 230–237, Newport Beach, CA., April 1993.

    Google Scholar 

  24. M. Wu and W. Shu. A dynamic program partitioning strategy on distributed memory systems. In Proceedings of the International Conference on Parallel Processing, volume I, pages 551–552, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana Champaign, 1304 W. Springfield Ave., 61801, Urbana, IL

    Laxmikant V. Kale, Ben H. Richards & Terry D. Allen

Authors
  1. Laxmikant V. Kale
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ben H. Richards
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Terry D. Allen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Takayasu Ito Robert H. Halstead Jr. Christian Queinnec

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kale, L.V., Richards, B.H., Allen, T.D. (1996). Efficient parallel graph coloring with prioritization. In: Ito, T., Halstead, R.H., Queinnec, C. (eds) Parallel Symbolic Languages and Systems. PSLS 1995. Lecture Notes in Computer Science, vol 1068. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023062

Download citation

  • DOI: https://doi.org/10.1007/BFb0023062

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61143-1

  • Online ISBN: 978-3-540-68332-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation