Distributed Detecting of Critical Nodes for Maximization of Connected Components in Wireless Multi-hop Networks

In Wireless Multi-hop Networks (WMhNs), nodes whose absence significantly weakens network connectivity or partitions the network into disconnected components are called critical nodes. This paper focuses on a critical node problem, the Maximizing the Number of Connected Components (MaxNum) problem, which aims to identify $k$ critical nodes whose removal maximizes the number of connected components. Although the MaxNum problem is a well-known NP-Hard problem with various real-world applications, no distributed algorithm has been proposed to solve it. To address this gap, we propose an efficient distributed algorithm for the MaxNum problem in WMhNs. The algorithm uses a distributed depth-first search tree to identify $k$ critical nodes, requiring a bit complexity of $O(n\times k\times {log}_{2}n)$ and a space complexity of $O(\Delta +k)$, where $\Delta$ denotes the maximum node degree. We evaluated the proposed algorithm through simulations and testbed networks, comparing it to the Linear Programming (LP) approach. Our findings show that the proposed distributed algorithm achieves promising outcomes, reaching nearly 90% of the optimal solution while reducing data transmission to half of that required by the centralized LP.