Abstract
We present fast distributed algorithms for coloring and (connected) dominating set construction in wireless ad hoc networks. We present our algorithms in the context of Unit Disk Graphs which are known to realistically model wireless networks. Our distributed algorithms take into account the loss of messages due to contention from simultaneous interfering transmissions in the wireless medium.
We present randomized distributed algorithms for (conflict-free) Distance-2 coloring, dominating set construction, and connected dominating set construction in Unit Disk Graphs. The coloring algorithm has a time complexity of O(Δ log2 n) and is guaranteed to use at most O(1) times the number of colors required by the optimal algorithm. We present two distributed algorithms for constructing the (connected) dominating set; the former runs in time O(Δ log 2 n) and the latter runs in time O(log 2 n). The two algorithms differ in the amount of local topology information available to the network nodes.
Our algorithms are geared at constructing Well Connected Dominating Sets (WCDS) which have certain powerful and useful structural properties such as low size, low stretch and low degree. In this work, we also explore the rich connections between WCDS and routing in ad hoc networks. Specifically, we combine the properties of WCDS with other ideas to obtain the following interesting applications:
-
An online distributed algorithm for collision-free, low latency, low redundancy and high throughput broadcasting.
-
Distributed capacity preserving backbones for unicast routing and scheduling.
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.: Connected dominating set and its induced position-less sparse spanner for mobile ad hoc networks. In: Proceedings of the Eighth IEEE Symposium on Computers and Communications (June 2003)
Alzoubi, K.M., Wan, P.-J., Frieder, O.: Distributed heuristics for connected dominating sets in wireless ad hoc networks. IEEE ComSoc/KICS Journal on Communication Networks 4, 22–29 (2002)
Alzoubi, K.M., Wan, P.-J., Frieder, O.: Message efficient construction of nontrivial connected dominating sets in wireless ad hoc networks. To appear in Special Issue of ACM Journal of Monet (2002)
Alzoubi, K.M., Wan, P.-J., Frieder, O.: Message-optimal connected-dominating-set construction for routing in mobile ad hoc networks. In: Proceedings of the Third ACM International Symposium on Mobile Ad Hoc Networking and Computing (June 2002)
Alzoubi, K.M., Wan, P.-J., Frieder, O.: New distributed algorithm for connected dominating set in wireless ad hoc networks. In: IEEE HICSS35 (2002)
Cheng, X., Huang, X., Li, D., Du, D.-Z.: Polynomial-time approximation scheme for minimum connected dominating set in ad hoc wireless networks. Technical report
Clark, B., Colbourn, C., Johnson, D.: Unit disk graphs. Discrete Mathematics 86, 165–177 (1990)
Das, B., Sivakumar, R., Bharghavan, V.: Routing in ad-hoc networks using a virtual backbone. In: 6th International Conference on Computer Communications and Networks IC3N 1997 (September 1997), pp. 1–20 (1997)
Das, B., Bharghavan, V.: Routing in ad-hoc networks using minimum connected dominating sets. ICC 1, 376–380 (1997)
Gandhi, R., Parthasarathy, S., Mishra, A.: Minimizing broadcast latency and redundancy in ad hoc networks. In: Proceedings of the fourth ACM international symposium on Mobile ad hoc networking and computing, pp. 222–232. ACM Press, New York (2003)
Gupta, P., Kumar, P.R.: The capacity of wireless networks. IEEE Transactions on Information Theory 46(2), 388–404 (2000)
Krumke, S.O., Marathe, M.V., Ravi, S.S.: Models and approximation algorithms for channel assignment in radio networks. Wireless Networks 7(6), 575–584 (2001)
Anil Kumar, V.S., Marathe, M.V., Parthasarathy, S., Srinivasan, A.: End-to-End Packet Scheduling in Ad Hoc Networks. To appear in ACM SODA (2004)
Luby, M.: A simple parallel algorithm for the maximal independent set problem. SIAM Journal on Computing 15(4), 1036–1053 (1986)
Luby, M.: Removing randomness in parallel computation without a processor penalty. Journal of Computer and System Sciences 47(2), 250–286 (1993)
Marathe, M.V., Breu, H., Hunt III, H.B., Ravi, S.S., Rosenkrantz, D.J.: Simple heuristics for unit disk graphs. Networks 25, 59–68 (1995)
Ramanathan, S.: A unified framework and algorithm for channel assignment in wireless networks. Wireless Networks 5(2), 81–94 (1999)
Ramanathan, S., Lloyd, E.L.: Scheduling algorithms for multihop radio networks. IEEE/ACM Transactions on Networking (TON) 1(2), 166–177 (1993)
Sen, A., Melesinska, E.: On approximation algorithms for radio network scheduling. In: Proceedings of the 35th Allerton Conference on Communication, Control and Computing, pp. 573–582 (1997)
Sivakumar, R., Das, B., Bharghavan, V.: Spine routing in ad hoc networks. ACM/Baltzer Cluster Computing Journal (special issue on Mobile Computing) (1998)
Wan, P.-J., Alzoubi, K., Frieder, O.: Distributed construction of connnected dominating set in wireless ad hoc networks. In: IEEE INFOCOM (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Parthasarathy, S., Gandhi, R. (2004). Distributed Algorithms for Coloring and Domination in Wireless Ad Hoc Networks. In: Lodaya, K., Mahajan, M. (eds) FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2004. Lecture Notes in Computer Science, vol 3328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30538-5_37
Download citation
DOI: https://doi.org/10.1007/978-3-540-30538-5_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24058-7
Online ISBN: 978-3-540-30538-5
eBook Packages: Computer ScienceComputer Science (R0)