A self-stabilising algorithm for 3-edge-connectivity

Authors:
Abusayeed M. Saifullah;Yung H. Tsin
Affiliations:
Computer and Inf. Science and Engineering, University of Florida, E301 CSE Building, P.O. Box 116120, Gainesville, FL 32611, USA/ Computer Science and Engineering Department, Washington University ...;School of Computer Science, University of Windsor, 401 Sunset Avenue, Windsor, Ontario N9C 3K7, Canada
Venue:
International Journal of High Performance Computing and Networking
Year:
2011

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Abstract

Self-stabilisation is a theoretical framework for fault-tolerance without external assistance. Adoption of self-stabilisation in distributed systems has received considerable research interest over the last decade. In this paper, we propose a self-stabilising algorithm for 3-edge-connectivity of an asynchronous distributed model of computation. A self-stabilising depth-first search algorithm is run concurrently to build a depth-first search spanning tree of the system. Once such a tree is constructed, all the 3-edge-connected components of the system can be detected in O(h) rounds, where h is the height of the depth-first search tree. The result of computation is kept in a distributed fashion in the sense that, upon stabilisation of the algorithm, each processor knows all other processors that are 3-edge-connected to it. The space complexity of our algorithm is O(n² log Δ) bits per processor, where Δ is an upper bound on the degree of a processor.