An optimal adaptive stabilizing algorithm for two edge-disjoint paths problem

Abstract

The problem of two edge-disjoint paths is to identify two paths $$Q_1$$Q1 and $$Q_2$$Q2 from source $$s \in V$$s?V to target $$t \in V$$t?V without any common arc in a directed connected graph $$G=(V, E)$$G=(V,E). In this paper, we present an adaptive stabilizing algorithm for finding a pair of edge-disjoint paths from s to t in G in O(D) rounds with state-space complexity of $$O(log\; n)$$O(logn) bits per process, where n is the number of nodes and D is the diameter of the graph. The proposed algorithm is optimal with respect to its time complexity, and the total length of the shortest paths. In addition, it can also be used to solve the problem for undirected graphs. 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. In addition, the proposed algorithm is adaptive since it is capable of dealing with topology changes in the form of addition/removal of arcs and/or nodes as well as changes in the directions of arcs provided that two edge-disjoint paths between s and t exist after the topology change.