A Self-Stabilizing Algorithm for a Maximal 2-Packing in a Cactus Graph Under Any Scheduler

Abstract

In this paper, we present a self-stabilizing algorithm that computes a maximal 2-packing set in a cactus under the adversarial scheduler. The cactus is a network topology such that any edge belongs to at most one cycle. The cactus has important applications in telecommunication networks, location problems, and biotechnology, among others. We assume that the value of each vertex identifier can take any value of length [Formula: see text] bits. The execution time of this algorithm is [Formula: see text] rounds or [Formula: see text] time steps. Our algorithm matches the state of the art results for this problem, following an entirely different approach. Our approach allows the computation of the maximum 2-packing when the cactus is a ring.