A Stabilizing Algorithm for Finding Two Node-Disjoint Paths in Arbitrary Networks

Abstract

The problem of two node-disjoint paths is to identify two paths [Formula: see text] and [Formula: see text] from source [Formula: see text] to target [Formula: see text] without any common intermediate node in a communication network [Formula: see text], where each node (vertex) in [Formula: see text] denotes a process and each edge [Formula: see text] denotes a communication channel between nodes [Formula: see text] and [Formula: see text]. In this paper, we present the first adaptive stabilizing algorithm for finding a pair of node-disjoint paths in a semi-anonymous arbitrary network in [Formula: see text] rounds and the state-space complexity is [Formula: see text] bits per process, where [Formula: see text] is the diameter of the communication network. The algorithm assumes weakly fair distributed daemon and the knowledge of an upper bound on the number of processes by each process. If two disjoint paths exist between [Formula: see text] and [Formula: see text], two disjoint paths are guaranteed to be constructed. In addition, the algorithm detects if two node-disjoint paths exist or not. Since the proposed algorithm is stabilizing, it does not require initialization and is capable of withstanding transient faults. We view a fault that perturbs the state of the system but not its program as a transient fault. The proposed algorithm has a wide range of applications in ensuring reliability and security of sensor, mobile and fixed communication networks.