This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
An Efficient Fault-Containing Self-Stabilizing Algorithm for Finding a Maximal Independent Set
August 2003 (vol. 14 no. 8)
pp. 742-754

Abstract—An independent set is a useful structure because, in some situations, it defines a set of mutually compatible operations, i.e., operations that can be executed simultaneously. In this paper, we design a fault-containing self-stabilizing algorithm that finds a maximal independent set for an asynchronuous distributed system. Our algorithm is an improvement on the self-stabilizing algorithm in Shukla et al.. In the single-fault situation, the worst-case stabilization time of Shukla's algorithm is \Omega(n), where n is the number of nodes in the system, whereas the worst-case stabilization time of our algorithm is O(\Delta), where \Delta is the maximum node degree in the system. Compared also with the fault-containing algorithm that is induced from applying the general transformer in Ghosh et al. to Shukla's algorithm, our algorithm is also seen to be faster in stabilization time, in the single-fault situation. Therefore, our algorithm can be considered to be the most efficient fault-containing self-stabilizing algorithm for the maximal independent set finding up to this point.

[1] Y. Afek and S. Dolev, Local Stabilizer J. Parallel and Distributed Computing, pp. 745-765, 2002.
[2] E.W. Dijkstra,“Self-stabilizing systems in spite of distributed control,” Comm. ACM, vol. 17, no. 11 pp. 643-644, 1974,.
[3] Edsger W. Dijkstra, Selected Writings on Computing: A Personal Perspective.New York: Springer Verlag, 1982, pp. 126-128.
[4] E.W. Dijkstra, A Belated Proof of Self-Stabilization Distributed Computing, vol. 1, no. 1, pp. 5-6, 1986.
[5] S. Ghosh and A. Gupta, “An Exercise in Fault-Containment: Self-Stabilizing Leader Election,” Information Processing Letters, vol. 59, pp. 281–288, 1996.
[6] S. Ghosh, A. Gupta, and T. Herman, Fault-Containing Self-Stabilizing Distributed Protocols unpublished manuscript, 2000.
[7] S. Ghosh, A. Gupta, and S.V. Pemmaraju, A Fault-Containing Self-Stabilizing Spanning Tree Algorithm J. Computing and Information, vol. 2, no. 1, pp. 322-338, 1996.
[8] S. Ghosh, A. Gupta, T. Herman, and S.V. Pemmaraju, “Fault-Containing Self-Stabilizing Algorithms,” Proc. 15th Ann. ACM Symp. Principles of Distributed Computing (PODC '96), pp. 45–54, 1996.
[9] A. Gupta, Fault-Containing in Self-Stabilizing Distributed Algorithm PhD thesis, Univ. of Iowa, 1997.
[10] S.K. Shukla, D.J. Rosenkrantz, and S.S. Ravi, Observations on Self-Stabilizing Graph Algorithms for Anonymous Networks Proc. WSS, pp. 1-15, 1995.

Index Terms:
Central demon, maximal independent set, single transient fault, fault-containment, restrictions on guard conditions, primary variables, auxiliary secondary variables, stabilization time, contamination number.
Citation:
Ji-Cherng Lin, Tetz C. Huang, "An Efficient Fault-Containing Self-Stabilizing Algorithm for Finding a Maximal Independent Set," IEEE Transactions on Parallel and Distributed Systems, vol. 14, no. 8, pp. 742-754, Aug. 2003, doi:10.1109/TPDS.2003.1225054
Usage of this product signifies your acceptance of the Terms of Use.