A Self-Stabilizing Algorithm for Finding Articulation Points

Abstract

In this paper, a self-stabilizing algorithm is presented for finding the articulation points of a connected undirected graph on a distributed or network model of computation after O(n2|E|) moves. The algorithm is resilient to transient faults and does not require initialization. A correctness proof of the algorithm is also presented. The paper concludes with remarks on issues such as the time complexity of the algorithm and open problems.

A Stabilizing Algorithm for Finding Biconnected Components

“…Self-stabilizing algorithms for electing a leader appear in [17,22]. Selfstabilizing algorithms for a variety of graph theoretic problems are presented in [7,13,20,19]. General techniques for constructing self-stabilizing algorithms are dealt with in [3,4,21].…”

Randomized Self-stabilizing Algorithms for Wireless Sensor Networks

“…Foremost these are algorithms for coloring, spanning trees, independent and dominating sets [5][6][7][8][9]. Furthermore, this work simplifies the design of self-stabilizing for WSNs, developers can work with the central daemon scheduler and do not have to take into considerations the imponderabilities of wireless communication.…”

“…Self-stabilization fits into the unattended operation style of WSNs, where no outside intervention is necessary. Over the last 20 years many self-stabilizing algorithms have been proposed, quite a few of them are of interest for WSNs: graph coloring [5], articulation points [6], dominating sets [7], depth-first trees [8], and spanning trees [9]. However, the majority of these algorithms is based on models not suitable for the constraints of WSNs: shared memory model, central daemon scheduler, unique processor identifiers, and atomicity.…”

An improved self-stabilizing algorithm for biconnectivity and bridge-connectivity

“…Once it is in a legitimate state, it stays in it for any subsequent fault free execution. Owing to this attractive feature, self-stabilizing algorithms for many fundamental problems have been proposed [1][2][3]5,[10][11][12]14].…”

“…Karaata [10] proposed the first self-stabilizing algorithm for finding cut-vertices. His algorithm must run concurrently with a self-stabilizing breadth-first spanning tree algorithm and the self-stabilizing bridge finding algorithm of Karaata and Chaudhuri [12].…”