Abstract
We introduce a new nature inspired algorithm to solve the Graph Coloring Problem (GCP): the Gravitational Swarm. The Swarm is composed of agents that act individually, but that can solve complex computational problems when viewed as a whole. We formulate the agent’s behavior to solve the GCP. Agents move as particles in the gravitational field defined by some target objects corresponding to graph node colors. Knowledge of the graph to be colored is encoded in the agents as friend-or-foe information. We discuss the convergence of the algorithm and test it over well-known benchmarking graphs, achieving good results in a reasonable time.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Akay, B., Karaboga, D.: A modified artificial bee colony algorithm for real-parameter optimization. Information Sciences, Corrected Proof (2010) (in press)
Brlaz, D.: New methods to color the vertices of a graph. Commun. ACM 22, 251–256 (1979)
Cases, B., Hernandez, C., Graña, M., D’anjou, A.: On the ability of swarms to compute the 3-coloring of graphs. In: Bullock, S., Noble, J., Watson, R., Bedau, M.A. (eds.) Artificial Life XI: Proceedings of the Eleventh International Conference on the Simulation and Synthesis of Living Systems, pp. 102–109. MIT Press, Cambridge (2008)
Chiarandini, M., Süttzle, T.: An application of iterated local search to graph coloring problem. In: Proceedings of the Computational Symposium on Graph Coloring and its Generalizations, Fachgebiet Intellektik, Fachbereich Informatik, and Technische Universitt Darmstadt Darmstadt, pp. 112–125 (2002)
Chvtal, V.: Coloring the queen graphs. Web repository (2004) (last visited July 2005)
Corneil, D.G., Graham, B.: An algorithm for determining the chromatic number of a graph. SIAM J. Comput. 2(4), 311–318 (1973)
Cui, G., Qin, L., Liu, S., Wang, Y., Zhang, X., Cao, X.: Modified pso algorithm for solving planar graph coloring problem. Progress in Natural Science 18(3), 353–357 (2008)
Dutton, R.D., Brigham, R.C.: A new graph colouring algorithm. The Computer Journal 24(1), 85–86 (1981)
Folino, G., Forestiero, A., Spezzano, G.: An adaptive flocking algorithm for performing approximate clustering. Information Sciences 179(18), 3059–3078 (2009)
Galinier, P., Hertz, A.: A survey of local search methods for graph coloring. Comput. Oper. Res. 33(9), 2547–2562 (2006)
Ge, F., Wei, Z., Tian, Y., Huang, Z.: Chaotic ant swarm for graph coloring. In: 2010 IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS), vol. 1, pp. 512–516 (2010)
Graña, M., Cases, B., Hernandez, C., D’Anjou, A.: Further results on swarms solving graph coloring. In: Taniar, D., Gervasi, O., Murgante, B., Pardede, E., Apduhan, B.O. (eds.) ICCSA 2010. LNCS, vol. 6018, pp. 541–551. Springer, Heidelberg (2010)
Handl, J., Meyer, B.: Ant-based and swarm-based clustering. Swarm Intelligence 1, 95–113 (2007)
Herrmann, F., Hertz, A.: Finding the chromatic number by means of critical graphs. J. Exp. Algorithmics 7, 10 (2002)
Hsu, L.-Y., Horng, S.-J., Fan, P., Khan, M.K., Wang, Y.-R., Run, R.-S., Lai, J.-L., Chen, R.-J.: Mtpso algorithm for solving planar graph coloring problem. Expert Syst. Appl. 38, 5525–5531 (2011)
Graay, M., Hernndez, C., Rebollo, I.: Aplicaciones de algoritmos estocasticos de otimizacin al problema de la disposicin de objetos no-convexos. Revista Investigacin Operacional 22(2), 184–191 (2001)
Johnson, D.S., Mehrotra, A., Trick, M. (eds.): Proceedings of the Computational Symposium on Graph Coloring and its Generalizations, Ithaca, New York, USA (2002)
Johnson, D.S., Trick, M.A.: Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, vol. 26. American Mathematical Society, Providence (1993)
Johnson, D.S., Trick, M.A. (eds.): Proceedings of the 2nd DIMACS Implementation Challenge. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26. American Mathematical Society, Providence (1996)
Lewandowski, G., Condon, A.: Experiments with parallel graph coloring heuristics and applications of graph coloring, pp. 309–334
Mehrotra, A., Trick, M.: A column generation approach for graph coloring. INFORMS Journal on Computing 8(4), 344–354 (1996)
Mizuno, K., Nishihara, S.: Toward ordered generation of exceptionally hard instances for graph 3-colorability, pp. 1–8
Mycielski, J.: Sur le coloureage des graphes. Colloquium Mathematicum 3, 161–162 (1955)
Reynolds, C.: Steering behaviors for autonomous characters (1999)
Reynolds, C.W.: Flocks, herds, and schools: A distributed behavioral model. In: Computer Graphics, pp. 25–34 (1987)
Sundar, S., Singh, A.: A swarm intelligence approach to the quadratic minimum spanning tree problem. Information Sciences 180(17), 3182–3191 (2010); Including Special Section on Virtual Agent and Organization Modeling: Theory and Applications
Turner, J.S.: Almost all k-colorable graphs are easy to color. Journal of Algorithms 9(1), 63–82 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ruiz, I.R., Romay, M.G. (2011). Gravitational Swarm Approach for Graph Coloring. In: Pelta, D.A., Krasnogor, N., Dumitrescu, D., Chira, C., Lung, R. (eds) Nature Inspired Cooperative Strategies for Optimization (NICSO 2011). Studies in Computational Intelligence, vol 387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24094-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-24094-2_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24093-5
Online ISBN: 978-3-642-24094-2
eBook Packages: EngineeringEngineering (R0)