Skip to main content

Solving Graph Coloring Problems Using Learning Automata

  • Conference paper
Evolutionary Computation in Combinatorial Optimization (EvoCOP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4972))

Abstract

The graph coloring problem (GCP) is a widely studied combinatorial optimization problem with numerous applications, including time tabling, frequency assignment, and register allocation. The growing need for more efficient algorithms has led to the development of several GCP solvers. In this paper, we introduce the first GCP solver that is based on Learning Automata (LA). We enhance traditional Random Walk with LA-based learning capability, encoding the GCP as a Boolean satisfiability problem (SAT). Extensive experiments demonstrate that the LA significantly improve the performance of RW, thus laying the foundation for novel LA-based solutions to the GCP.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Narendra, K.S., Thathachar, M.A.L.: Learning Automata: An Introduction. Prentice Hall, Englewood Cliffs (1989)

    Google Scholar 

  2. Selman, B., Kautz, H.A., Cohen, B.: Noise Strategies for Improving Local Search. In: Proceedings of AAAI 1994, pp. 337–343. MIT Press, Cambridge (1994)

    Google Scholar 

  3. Gamst, A.: Some lower bounds for a class of frequency assignment problems. IEEE Transactions of Vehicular Technology 35, 8–14 (1986)

    Article  Google Scholar 

  4. Chow, F., Hennessy, J.: The priority-based coloring approach to register allocation. ACM Transactions on Programming Languages and Systems 12, 501–536 (1990)

    Article  Google Scholar 

  5. Ogawa, H.: Labeled point pattern matching by delaunay triangulation and maximal cliques. Pattern Recognition 19, 35–40 (1996)

    Article  Google Scholar 

  6. Werra, D.D.: An introduction to timetabling. European Journal of Operations Research 19, 151–162 (1985)

    Article  MATH  Google Scholar 

  7. Gebremedhin, A., Manne, F., Pothen, A.: What color is your jacobian? graph coloring for computing derivatives. SIAM Review 47, 629–705 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Cook, S.: The complexity of theorem-proving procedures. In: Proceedings of the Third ACM Symposuim on Theory of Computing, pp. 151–158 (1971)

    Google Scholar 

  9. Tsetlin, M.L.: Automaton Theory and Modeling of Biological Systems. Academic Press, London (1973)

    Google Scholar 

  10. Caramia, M., Dell’Olmo, P.: Bounding vertex coloring by truncated multistage branch and bound. Networks 44, 231–242 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Mehrotra, A., Trick, M.A.: A column generation approach for graph coloring. INFORMS Journal on Computing 8, 344–354 (1996)

    Article  MATH  Google Scholar 

  12. Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM 7, 201–215 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  13. Selman, B., Levesque, H., Mitchell, D.: A new method for solving hard satisfiability problems. In: Proceedings of AAA 1992, pp. 440–446. MIT Press, Cambridge (1992)

    Google Scholar 

  14. McAllester, D., Selman, B., Kautz, H.: Evidence for Invariants in Local Search. In: Proceedings of AAAI 1997, pp. 321–326. MIT Press, Cambridge (1997)

    Google Scholar 

  15. Glover, F.: Tabu search-part 1. ORSA Journal on Computing 1, 190–206 (1989)

    MATH  MathSciNet  Google Scholar 

  16. Oommen, B.J., Ma, D.C.Y.: Deterministic learning automata solutions to the equipartitioning problem. IEEE Transactions on Computers 37(1), 2–13 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  17. Gale, W., Das, S., Yu, C.: Improvements to an Algorithm for Equipartitioning. IEEE Transactions on Computers 39, 706–710 (1990)

    Article  Google Scholar 

  18. Oommen, B.J., Croix, E.V.S.: Graph partitioning using learning automata. IEEE Transactions on Computers 45(2), 195–208 (1996)

    Article  MATH  Google Scholar 

  19. Granmo, O.C., Oommen, B.J., Myrer, S.A., Olsen, M.G.: Learning Automata-based Solutions to the Nonlinear Fractional Knapsack Problem with Applications to Optimal Resource Allocation. IEEE Transactions on Systems, Man, and Cybernetics Part B (2006)

    Google Scholar 

  20. Oommen, B.J., Hansen, E.R.: List organizing strategies using stochastic move-to-front and stochastic move-to-rear operations. SIAM Journal on Computing 16, 705–716 (1987)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jano van Hemert Carlos Cotta

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bouhmala, N., Granmo, OC. (2008). Solving Graph Coloring Problems Using Learning Automata. In: van Hemert, J., Cotta, C. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2008. Lecture Notes in Computer Science, vol 4972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78604-7_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-78604-7_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78603-0

  • Online ISBN: 978-3-540-78604-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics