Random leaders and random spanning trees

Abstract

The problem of distributively constructing a minimum spanning tree has been thoroughly studied. The root of this spanning tree is often elected as a leader, and then centralized algorithms are run in the distributed system. If, however, we have fault tolerance in mind, selecting a random spanning tree and a random leader are more desirable. If we manage to select a random tree, the probability that a bad channel will disconnect some nodes from the random tree is relatively small. Otherwise, a small number of predetermined edges will greatly effect the system's behavior. In this paper we present an algorithm for choosing a random leader (RL), and distributed random spanning tree algorithms (RST), where random means, that each spanning tree in the underlying graph has the same probability of being selected. We give optimal algorithms for the complete graph and the ring. We also describe an RST algorithm for the general graph, and discuss the relation between RST and RL algorithms.