Distributed Generalized Graph Coloring

We consider generalized coloring of a weighted graph in a distributed setting, where each node in the graph is represented by an independent agent. The target is to minimize the weight of edges connecting same-color nodes. To avoid getting stuck in a not-too-good local optimum, we approach this problem by finding the colorable sub graph with the maximum weight subset of edges. The agents run a basic distributed graph coloring algorithm, and an algorithm for adding and removing edges, operating on different time scales. As basic distributed algorithms to color graphs we use distributed local search algorithms enabling plateau walks, together with a noise strategy to escape local minima. We evaluate performance in a setting inspired by self-organized resource allocation in a wireless network, and show that a distributed algorithm finding a colorable sub graph can outperform distributed greedy local search. As a related sub-problem, we investigate a procedure of adding edges to random planar graphs, keeping the color ability.