An Efficient Parallel Algorithm for finding Bridges in a Dense Graph

TL;DR

This paper introduces a parallel algorithm optimized for dense graphs that efficiently finds bridges and failure points in distributed environments by generating sparse certificates and using DFS on compressed subgraphs.

Contribution

It presents a novel parallel approach for identifying bridges in dense graphs using graph decomposition and DFS, optimized for distributed systems.

Findings

Achieves O(E/M + Vlog(M)) time complexity on M machines.

Effectively decomposes dense graphs into minimal subgraphs.

Provides a scalable method for failure point detection in networks.

Abstract

This paper presents a simple and efficient approach for finding the bridges and failure points in a densely connected network mapped as a graph. The algorithm presented here is a parallel algorithm which works in a distributed environment. The main idea of our algorithm is to generate a sparse certificate for a graph and finds bridges using a simple DFS (Depth First Search). We first decompose the graph into independent and minimal subgraphs using a minimum spanning forest algorithm. To identify the bridges in the graph network, we convert these subgraphs into a single compressed graph and use a DFS approach to find bridges. The approach presented here is optimized for the use cases of dense graphs and gives the time complexity of O(E/M + Vlog(M)), for a given graph G(V,E) running on M machines.