Abstract
Our purpose in this paper is to propose a self-stabilizing protocol for weakly connected dominating set (WCDS) set in a given ad hoc network graph. WCDS is a particular variant of graph domination predicates which play an important role in routing in ad hoc networks. There are many variants of domination problems in bidirectional networks; WCDS is also useful in forming clusters in ad hoc networks. There are many heuristic and distributed algorithms to compute WCDS in network graphs while almost all of them will need complete information about the network topology and most of them are not fault tolerant or mobility tolerant. Self-stabilization is a protocol design paradigm that is especially useful in resource constrained infrastructure-less networks since nodes can make moves based on local knowledge only and yet a global task is accomplished in a fault tolerant manner; it also facilitates for nodes to enter and exit the network freely. There exist self-stabilizing protocols for minimal spanning tree, total domination, and others. We have shown that the paradigm is capable of designing a protocol for WCDS. Our objective is to mathematically prove the correctness and the convergence of the protocol in any worst-case scenario, as is usually done for self-stabilizing protocols for other graph predicates used for ad hoc networks.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Estrin D, Govindan R, Heidemann JS, Kumar S (1999) Next century challenges: scalable coordination in sensor networks. In: Mobile computing and networking, pp 263–270
Attiya H, Welch J (1998) Distributed computing: fundamentals, simulations and advanced topics. McGraw-Hill, New York
Haynes TW, Hedetniemi ST, Slater PJ (1998) Fundamentals of domination in graphs. Marcel Dekker, New York
Dolev S, Israeli A, Moran S (1993) Self-stabilization of dynamic systems assuming only read/write atomicity. Distrib Comput 7:3–16
Chen NS, Yu HP, Huang ST (1991) A self-stabilizing algorithm for constructing spanning trees. Inf Process Lett 39(3):147–151
Sur S, Srimani PK (1992) A self-stabilizing distributed algorithm to construct BFS spanning trees of a symmetric graph. Parallel Process Lett 2(23):171–179
Arora A, Gouda M (1994) Distributed reset. IEEE Trans Comput 43(9):1026–1038
Guha S, Khuller S (1998) Approximation algorithms for connected domination sets. Algorithmica 20(4):374–387
Wan P-J, Alzoubi K, Frieder O (2002) Distributed construction of connected dominating set in wireless ad hoc networks. In: Proceedings of IEEE INFOCOM, vol 3, June 2002, pp 1597–1604
Dai F, Wu J (2004) An extended localized algorithm for connected dominating set formation in ad hoc wireless networks. IEEE Trans Parallel Distrib Syst 15(10):908–920
Frieder O, Alzoubi KM, Wan P-J (2003) Weakly-connected dominating sets and sparse spanners in wireless ad hoc networks. In: 23rd IEEE international conference on distributed computing systems (ICDCS’03), 2003, p 96
Dubhashi D, Mei A, Panconesi A, Radhakrishnan J, Srinivasan A (2003) Fast distributed algorithms for (weakly) connected dominating sets and linear-size skeletons. In: Proc 14th annual ACM-SIAM symp on discrete algorithms, 2003, pp 717–724
Turau V (2007) Linear self-stabilizing algorithms for the independent and dominating set problems using an unfair distributed scheduler. Inf Process Lett, 88–93
Swaminathan V (2009) Weakly connected domination in graphs. Discrete Math 33:67–73
Han B, Jia W (2007) Clustering wireless ad hoc networks with weakly connected dominating set. J Parallel Distrib Comput 67:727–737
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xu, Z., Wang, J. & Srimani, P.K. Distributed fault tolerant computation of weakly connected dominating set in ad hoc networks. J Supercomput 53, 182–195 (2010). https://doi.org/10.1007/s11227-009-0325-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11227-009-0325-2