Self-Stabilizing Topology Computation (Identification) of Cactus Graphs Using Master Slave Token Circulation

Abstract

In this paper we propose a self stabilizing algorithm to compute the topology of a given arbitrary cactus graph; we use the most recent self stabilizing algorithm for token circulation in Cactus graphs [2] and design the proposed algorithm by making a single token traverse the graph multiple times and accumulating the topology information at the master node incrementally after each round in a space efficient way. The topology computation is completed in $O(n^{2})$ steps with $O (\Delta)$ bits extra storage at each node, where n is the number of nodes in the graph, and $\\lt p\gt Delta$ is the maximum degree of the cactus graph.