Distributed Detection of Minimum Cuts in Wireless Multi-Hop Networks

Abstract

Communicating over multi-hop connections simplifies the establishment of wireless multi-hop networks but brings new challenges such as limited reliability, bottlenecks, and weak connections. The minimum cut of a graph is the smallest subset of edges whose removal disconnects some nodes from the others. Finding minimum cuts of a wireless multi-hop network may reveal useful information such as bottlenecks and critical areas. This article introduces a distributed algorithm for detecting minimum cuts of a given witless multi-hop network by finding available edge-disjoint paths. Initially, the paths between two arbitrary neighbors are detected and these nodes are grouped as visited nodes. Then, the other nodes are added to the visited group one by one by finding at most <inline-formula><tex-math notation="LaTeX">$O(n)$</tex-math></inline-formula> paths in total where <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is the number of nodes. The comprehensive simulation results showed that the proposed asynchronous algorithm detects minimum cuts with up to 37.1 and 55.8 percent lower sent bytes than the existing synchronous and central algorithms, respectively.