Abstract
Given a graph G, a k-dominating set of G is a subset S of its vertices with the property that every vertex of G is either in S or has at least k neighbors in S. We present a new incremental distributed algorithm to construct a k-dominating set. The algorithm constructs a monotone family of dominating sets D 1 ⊆ D 2... ⊆ D i ... ⊆ D k such that each D i is an i-dominating set. For unit disk graphs, the size of each of the resulting i-dominating sets is at most six times the optimal.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alzoubi, K.M., Wan, P.-J., Frieder, O.: Message-optimal connected dominating sets in mobile ad hoc networks. In: MobiHoc 2002: Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing, pp. 157–164. ACM Press, New York (2002)
Couture, M., Barbeau, M., Bose, P., Kranakis, E.: Incremental construction of k-dominating sets in wireless sensor networks. Tech. Rep. TR-06-11, School of Computer Science, Carleton University, Ottawa, Ontario, Canada (2006)
Dai, F., Wu, J.: On constructing k-connected k-dominating set in wireless networks. In: IPDPS. IEEE Computer Society, Los Alamitos (2005)
Johnson, D.S.: Approximation algorithms for combinatorial problems. In: STOC 1973: Proceedings of the fifth annual ACM symposium on Theory of computing, pp. 38–49. ACM Press, New York (1973)
Kuhn, F.: The Price of Locality: Exploring the Complexity of Distributed Coordination Primitives. PhD Thesis, ETH Zurich, Diss. ETH No. 16213 (2005)
Kuhn, F., Moscibroda, T., Wattenhofer, R.: What cannot be computed locally! In: PODC 2004: Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing, pp. 300–309. ACM Press, New York (2004)
Kuhn, F., Moscibroda, T., Wattenhofer, R.: On the locality of bounded growth. In: PODC 2005: Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing, pp. 60–68. ACM Press, New York (2005)
Kuhn, F., Moscibroda, T., Wattenhofer, R.: Fault-Tolerant Clustering in Ad Hoc and Sensor Networks. In: 26th International Conference on Distributed Computing Systems (ICDCS), Lisboa, Portugal (2006)
Marathe, M., Breu, H., Ravi, S., Rosenkrantz, D.: Simple heuristics for unit disk graphs. Networks 25, 59–68 (1995)
Penrose, M.D.: The longest edge of the random minimal spanning tree. The Annals of Applied Probability 7(2), 340–361 (1997)
Penrose, M.D.: On k-connectivity for a geometric random graph. Random Struct. Algorithms 15(2), 145–164 (1999)
Stojmenovic, I., Seddigh, M., Zunic, J.: Dominating sets and neighbor elimination-based broadcasting algorithms in wireless networks. IEEE Trans. Parallel Distrib. Syst. 13(1), 14–25 (2002)
Wan, P.-J., Alzoubi, K.M., Frieder, O.: Distributed construction of connected dominating set in wireless ad hoc networks. Mob. Netw. Appl. 9(2), 141–149 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Couture, M., Barbeau, M., Bose, P., Kranakis, E. (2006). Incremental Construction of k-Dominating Sets in Wireless Sensor Networks. In: Shvartsman, M.M.A.A. (eds) Principles of Distributed Systems. OPODIS 2006. Lecture Notes in Computer Science, vol 4305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11945529_15
Download citation
DOI: https://doi.org/10.1007/11945529_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49990-9
Online ISBN: 978-3-540-49991-6
eBook Packages: Computer ScienceComputer Science (R0)