Leader Election by d Dimensional Cellular Automata

We present a cellular algorithm in O(w2) for the leader election problem on a finite connected subset F of Zd of excentricity w, for any fixed d. The problem consists in finding an algorithm such that when setting the elements of F to a special state, and all the others to a state #, the cellular automaton iterates a finite number of steps and eventually sets only one precise element of F to a special state called leader state, and all the others to a different state. We describe the algorithm in detail, outline its proof and complexity, and discuss the possible extensions on more general Cayley graphs.