A Self-stabilizing Algorithm For 3-Edge-Connectivity

Abstract

The adoption of self-stabilization as an approach to fault-tolerant behavior has received considerable research interest over the last decade. In this paper, we propose a self-stabilizing algorithm for 3-edge-connectivity of an asynchronous distributed model of computation. The self-stabilizing depth-first search algorithm of Collin and Dolev [4] is run concurrently to build a depth-first search spanning tree of the system. Once such a tree of height h is constructed, the detection of all 3-edge-connected components of the system requires O(h) rounds. The result of computation is kept in a distributed fashion in the sense that, upon stabilization of another phase of the algorithm, each processor knows all other processors that are 3-edge-connected to it. Until now, this is the only algorithm to compute all the 3-edge-connected components in the context of self-stabilization. Assuming that every processor requires m bits for the depth-first search algorithm, the space complexity of our algorithm is O(hm) bits per processor.