Abstract
We have proposed the mapping of graph coloring problems into swarm dynamics. Empirical evidence that flock steering behaviors augmented with the notion of hostility (enmity and friendliness) are enough to perform efficiently the task of coloring the nodes of graphs even in the case 3-coloration hard graph topologies. We discuss here what are the minimal cognitive capabilities that allow the emergent behavior of swarms to solve such NP-complete problem without mediating an explicit knowledge representation.
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
Brélaz, D.: New methods to color vertices of a graph. Communications of 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)
Diestel, R.: Graph Theory, electronic edn. Springer, USA (2005)
Dorigo, M., Blum, C.: Ant Colony Optimization theory: a survey. Theorical Computer Science 344, 243–278 (2005)
Dorigo, M., Gambardella, L.M.: Ant Colonies for the Traveling Salesman Problem. BioSystems 43, 73–81 (1997)
Galinier, P., Hertz, A.: A survey of local search methods for graph coloring. Comput. Oper. Res. 33, 2547–2562 (2006)
Galinier, P., Hertz, A., Zufferey, N.: An adaptive memory algorithm for the k-coloring problem. Discrete Applied Mathematics 156(2), 267–279 (2008)
Mizuno, K., Nishihara, S.: Constructive generation of very hard 3-colorability instances. Discrete Applied Mathematics 156(2), 218–229 (2008)
Reynolds, C.W.: Flocks, herds, and schools: A distributed behavioral model. Computer Graphics 21, 25–34 (1987)
Reynolds, C.W.: Steering Behaviors for Autonomous Characters (1999), http://www.red3d.com/cwr/papers/1999/gdc99steer.html
Smith, J.M.: Evolution and the theory of games. Cambridge University Press, Cambridge (1992)
Smith, J.M., Price, G.R.: The logic of animal conflict. Nature 246 (November)
Turk, G.: Generating textures on arbitrary surfaces using reaction-diffusion. SIGGRAPH Computers Graphics 25(4), 289–298 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Graña, M., Cases, B., Hernandez, C., D’Anjou, A. (2010). Further Results on Swarms Solving Graph Coloring. In: Taniar, D., Gervasi, O., Murgante, B., Pardede, E., Apduhan, B.O. (eds) Computational Science and Its Applications – ICCSA 2010. ICCSA 2010. Lecture Notes in Computer Science, vol 6018. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12179-1_44
Download citation
DOI: https://doi.org/10.1007/978-3-642-12179-1_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12178-4
Online ISBN: 978-3-642-12179-1
eBook Packages: Computer ScienceComputer Science (R0)