Distributed computing with advice: information sensitivity of graph coloring

We study the problem of the amount of information (advice) about a graph that must be given to its nodes in order to achieve fast distributed computations. The required size of the advice enables to measure the information sensitivity of a network problem. A problem is information sensitive if little advice is enough to solve the problem rapidly (i.e., much faster than in the absence of any advice), whereas it is information insensitive if it requires giving a lot of information to the nodes in order to ensure fast computation of the solution. In this paper, we study the information sensitivity of distributed graph coloring. A preliminary version of this paper appeared in the proceedings of the 34th International Colloquium on Automata, Languages and Programming (ICALP), July 2007. A part of this work was done during the stay of David Ilcinkas at the Research Chair in Distributed Computing of the Université du Québec en Outaouais, as a postdoctoral fellow. P. Fraigniaud received additional support from the ANR project ALADDIN. A. Pelc was supported in part by NSERC discovery grant and by the Research Chair in Distributed Computing of the Université du Québec en Outaouais.