An adaptive stabilizing algorithm for finding all disjoint paths in anonymous mesh networks

Abstract

In this paper, we present an adaptive stabilizing algorithm for finding all disjoint paths in anonymous mesh networks. Given two distinct nodes s and t of a network, the all disjoint paths problem is to identify all disjoint paths from s to t. Since our algorithm is stabilizing, it does not require initialization and withstands transient faults. In addition, the proposed algorithm adapts to topology changes in the form of process/link crashes and additions, i.e., upon a topology change, it finds all available paths from s to t. The space complexity of our algorithm is 4 × d states for the source process s, one state for the target process, 120 × d states for other processes, where d is the diameter of the communication network. The time complexity of the proposed algorithm is O ( d ) rounds. The proposed algorithm has a wide range of applications in ensuring reliability and security of sensor, mobile and fixed communication networks.