Optimal-election algorithms for hypercubes

Leader election is a fundamental problem in distributed computing and regards a wide number of applications. In order to solve this problem, it is possible and convenient to exploit the topological properties of the specific distributed systems, so to reduce time and message complexity. In this paper we study the problem of leader election in a hypercube network on the assumption that the system possesses a sense of direction, i.e. it is capable to distinguish between adjacent communication links; to demonstrate, two new optimal algorithms are presented. The correctness of the proposed algorithms is not constrained by the simultaneous activation of a subset of the processors in the network but the awake of only one processor suffices. The time and message complexity shown by both algorithms lets them be competitive compared to other solutions found in literature.