ADA-PC: An asynchronous distributed algorithm for minimizing pairwise connectivity in wireless multi-hop networks

Reliability analysis is of great significance to designing and maintaining wireless multi-hop networks (WMhNs). In WMhNs, several reasons can cause a node to be inoperable, such as hardware failure, software errors, and battery drain. Failure of some critical nodes may partition networks into disconnected segments. The presence of such critical nodes may also reduce the network lifetime since they consume more energy for packet forwarding. Therefore, it is crucial to identify the critical nodes of the networks and strengthen them by adding more nodes surrounding those or creating alternate pathways connecting other nodes to ensure connectivity maintenance in WMhNs. One of the most common approaches in direction is detecting the cut nodes of the networks. However, although finding cut nodes provide helpful information, it may be insufficient for precise reliability analysis since finding cut nodes only does not consider the remaining network. Critical Node Problem (CNP) aims to detect the most important nodes of the network whose removal minimizes the pairwise connectivity (the total number of node pairs connected by at least one path). In other words, the CNP tries to identify a set of nodes whose absence partitions the network into several disconnected segments of similar size. Detecting critical nodes for pairwise connectivity reveals the weak points and bottlenecks of the networks and may help to increase the fault tolerance and lifetime of WMhNs. This paper proposes an Asynchronous Distributed Algorithm for minimizing Pairwise Connectivity (ADA-PC) in WMhNs. To the best of our knowledge, this is the first distributed algorithm for the targeted problem in the network literature. The proposed algorithm uses a distributed Breadth-First Search (BFS) tree which limits bit complexity to O(n.m.log2n) and space complexity to O(d), where d is the network's diameter. The experimental study on both testbed experiment and simulation reveals that the proposed algorithm is capable of finding the most critical nodes with up to 60% lower sent bytes than the existing central algorithms.