Self-Stabilizing Computation of 3-Edge-Connected Components

A self-stabilizing algorithm is a distributed algorithm that can start from any initial (legitimate or illegitimate) state and eventually converge to a legitimate state in finite time without being assisted by any external agent. In this paper, we propose a selfstabilizing algorithm for finding the 3-edge-connected components of an asynchronous distributed computer network. The algorithm stabilizes in O(dn∆) rounds and every processor requires O(n log∆) bits, where ∆(≤ n) is an upper bound on the degree of a node, d(≤ n) is the diameter of the network, and n is the total number of nodes in the network. These time and space complexity are at least a factor of n better than those of the previously best-known self-stabilizing algorithm for 3-edge-connectivity. The result of the computation is kept in a distributed fashion by assigning, upon stabilization of the algorithm, a component identifier to each processor which uniquely identifies the 3edge-connected component to which the processor belongs. Furthermore, the algorithm is designed in such a way that its time complexity is dominated by that of the self-stabilizing depth-first search spanning tree construction in the sense that any improvement made in the latter automatically implies improvement in the time complexity of the algorithm.