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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Narendra, K.S., Thathachar, M.A.L.: Learning Automata: An Introduction. Prentice Hall, Englewood Cliffs (1989)
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)
Gamst, A.: Some lower bounds for a class of frequency assignment problems. IEEE Transactions of Vehicular Technology 35, 8–14 (1986)
Chow, F., Hennessy, J.: The priority-based coloring approach to register allocation. ACM Transactions on Programming Languages and Systems 12, 501–536 (1990)
Ogawa, H.: Labeled point pattern matching by delaunay triangulation and maximal cliques. Pattern Recognition 19, 35–40 (1996)
Werra, D.D.: An introduction to timetabling. European Journal of Operations Research 19, 151–162 (1985)
Gebremedhin, A., Manne, F., Pothen, A.: What color is your jacobian? graph coloring for computing derivatives. SIAM Review 47, 629–705 (2005)
Cook, S.: The complexity of theorem-proving procedures. In: Proceedings of the Third ACM Symposuim on Theory of Computing, pp. 151–158 (1971)
Tsetlin, M.L.: Automaton Theory and Modeling of Biological Systems. Academic Press, London (1973)
Caramia, M., Dell’Olmo, P.: Bounding vertex coloring by truncated multistage branch and bound. Networks 44, 231–242 (2004)
Mehrotra, A., Trick, M.A.: A column generation approach for graph coloring. INFORMS Journal on Computing 8, 344–354 (1996)
Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM 7, 201–215 (1960)
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)
McAllester, D., Selman, B., Kautz, H.: Evidence for Invariants in Local Search. In: Proceedings of AAAI 1997, pp. 321–326. MIT Press, Cambridge (1997)
Glover, F.: Tabu search-part 1. ORSA Journal on Computing 1, 190–206 (1989)
Oommen, B.J., Ma, D.C.Y.: Deterministic learning automata solutions to the equipartitioning problem. IEEE Transactions on Computers 37(1), 2–13 (1988)
Gale, W., Das, S., Yu, C.: Improvements to an Algorithm for Equipartitioning. IEEE Transactions on Computers 39, 706–710 (1990)
Oommen, B.J., Croix, E.V.S.: Graph partitioning using learning automata. IEEE Transactions on Computers 45(2), 195–208 (1996)
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)
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)
Author information
Authors and Affiliations
Editor information
Rights 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)