# Distributed graph coloring: an approach based on the calling behavior of Japanese tree frogs

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## Abstract

Graph coloring—also known as vertex coloring—considers the problem of assigning colors to the nodes of a graph such that adjacent nodes do not share the same color. The optimization version of the problem concerns the minimization of the number of colors used. In this paper we deal with the problem of finding valid graphs colorings in a distributed way, that is, by means of an algorithm that only uses local information for deciding the color of the nodes. The algorithm proposed in this paper is inspired by the calling behavior of Japanese tree frogs. Male frogs use their calls to attract females. Interestingly, groups of males that are located near each other desynchronize their calls. This is because female frogs are only able to correctly localize male frogs when their calls are not too close in time. The proposed algorithm makes use of this desynchronization behavior for the assignment of different colors to neighboring nodes. We experimentally show that our algorithm is very competitive with the current state of the art, using different sets of problem instances and comparing to one of the most competitive algorithms from the literature.

## Keywords

Distributed graph coloring Calling behavior of Japanese tree frogs## Notes

### Acknowledgements

The authors greatly appreciate the help by Enrico Malaguti who kindly provided experimental results of the centralized algorithm from Malaguti et al. (2008) for all problem instances.

Furthermore, we would like to thank Martin Middendorf who made us aware of the literature dealing with the calling behavior of Japanese tree frogs.

Finally, it is mandatory to mention the work of the Editor, Marco Dorigo, and the anonymous reviewers, who did a great job in helping to fine-tune the paper.

This work was supported by grant TIN2007-66523 (FORMALISM) of the Spanish government, and by the EU project FRONTS (FP7-ICT-2007-1). In addition, C. Blum acknowledges support from the *Ramón y Cajal* program of the Spanish Government, and H. Hernández acknowledges support from the *Comissionat per a Universitats i Recerca del Departament d’Innovació, Universitats i Empresa de la Generalitat de Catalunya* and from the *European Social Fund*.

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