2-Edge-Connectivity and 2-Vertex-Connectivity with Fault Containment

Self-stabilization for non-masking fault-tolerant distributed system has received considerable research interest over the last decade. In this paper, we propose a self-stabilizing algorithm for 2-edge-connectivity and 2-vertex-connectivity of an asynchronous distributed computer network. It is based on a self-stabilizing depth-first search, and is not a composite algorithm in the sense that it is not composed of a number of self-stabilizing algorithms that run concurrently. The time and space complexities of the algorithm are the same as those of the underlying self-stabilizing depth-first search algorithm

Finding 3-edge-connected components in parallel

A parallel algorithm for finding 3-edge-connected components of an undirected graph on a CRCW PRAM is presented. The time and work complexity of this algorithm is O(logn) and O((m+n)loglogn), respectively, where n is the number of vertices and m is the number of edges in the input graph. The algorithm is based on ear decomposition and reduction of 3-edge-connectivity to 1-vertex-connectivity. This is the first 3-edge-connected component algorithm of a parallel model

A Distributed Algorithm for Finding Separation Pairs in a Computer Network

One of the main problems in graph theory is graph connectivity which is often studied for network reliability problems.It can be studied from two aspects, vertex-connectivity and edge-connectivity. Vertex connectivity is the smallest number of vertices whose deletion will cause a connected graph to be disconnected. We focus our work on finding separation pairs of a graph which is the set of pairs of vertices that deleting them would disconnect a graph. Finding separation pairs can be used in solving vertex-connectivity problem and finding the triconnected components of the graph. The algorithms presented during the past are non-linear or if linear, very complicated. This work is based on Tarjan and Hopcroft\u27s paper which uses Depth-First Search and finds the separation pairs in linear time. Our goal is to present an algorithm that finds the separation pairs in an asynchronous distributed computer network using distributed Depth-First search (DDFS)