Distributed Graph Coloring: An Approach Based on the Calling Behavior of Japanese Tree Frogs

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 used colors. In this paper we deal with the problem of finding valid colorings of graphs in a distributed way, that is, by means of an algorithm that only uses local information for deciding the color of the nodes. Such algorithms prescind from any central control. Due to the fact that quite a few practical applications require to find colorings in a distributed way, the interest in distributed algorithms for graph coloring has been growing during the last decade. As an example consider wireless ad-hoc and sensor networks, where tasks such as the assignment of frequencies or the assignment of TDMA slots are strongly related to graph coloring. 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 nearby each other desynchronize their calls. This is because female frogs are only able to correctly localize the male frogs when their calls are not too close in time. 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.