Leader election and centers and medians in tree networks

Abstract

We give a weak leader election algorithm, which elects a leader or two neighboring co-leaders of an anonymous tree network, as well as give distributed algorithms for finding centers and medians of anonymous tree networks. All algorithms are in the comparison model, are self-stabilizing and silent under the unfair daemon. Each of the three problems is solved in O(Diam) rounds with step complexity O(n • Diam). The per process space complexity is O(1) for weak leader election, O(log Diam) for finding centers, and O(log n) for finding medians. These are the minimum possible space complexities for self-stabilizing silent algorithms. The main innovation is the introduction of the constant space implementation of parent pointers using the finite Abelian group ℤ5. © Springer International Publishing 2013.