Distributed local 2-connectivity test of graphs and applications

Authors:
Brahim Hamid;Bertrand Le Saëc;Mohamed Mosbah
Affiliations:
LaBRI-University of Bordeaux-1, Talence, France;LaBRI-University of Bordeaux-1, Talence, France;LaBRI-University of Bordeaux-1, Talence, France
Venue:
ISPA'07 Proceedings of the 5th international conference on Parallel and Distributed Processing and Applications
Year:
2007

Citing 6
Cited 1

Graph relabelling systems and distributed algorithms

Handbook of graph grammars and computing by graph transformation
Computing vertex connectivity: new bounds from old techniques

Journal of Algorithms
Distributed computing: fundamentals, simulations and advanced topics

Distributed computing: fundamentals, simulations and advanced topics
Introduction to Distributed Algorithms

Introduction to Distributed Algorithms
Revisiting the Paxos Algorithm

WDAG '97 Proceedings of the 11th International Workshop on Distributed Algorithms
Using expander graphs to find vertex connectivity

FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science

Distributed overlay maintenance with application to data consistency

Globe'11 Proceedings of the 4th international conference on Data management in grid and peer-to-peer systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

The vertex connectivity of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. This work is devoted to the problem of vertex connectivity test of graphs in a distributed environment based on a constructive approach. The contribution of this paper is threefold. First, using a pre-constructed spanning tree of the considered graph, we present a protocol to test whether a given graph is 2-connected using only local knowledge. Second, we present an encoding of this protocol using graph relabeling systems. The last contribution is the implementation of this protocol in the message passing model. For a given graph G, where M is the number of its edges, N the number of its nodes and Δ is its degree, our algorithms need the following requirements: The first one uses O(Δ×N2) steps and O(Δ×logΔ) bits per node. The second one uses O(Δ × N2) messages and O(N2) time and O(Δ×logΔ) bits per node. Furthermore, the studied network is semi-anonymous: Only the root of the pre-constructed spanning tree needs to be identified. Moreover, we investigate some applications that can use our protocol as a pre-processing task for initial configurations.