Abstract
Consider the following classical problem in ad-hoc networks: n devices are distributed uniformly at random in a given region. Each device is allowed to choose its own transmission radius, and two devices can communicate if and only if they are within the transmission radius of each other. The aim is to (quickly) establish a connected network of low average and maximum degree.
In this paper we present the first efficient distributed protocols that, in poly-logarithmically many rounds and with high probability, set up a connected network with O(1) average degree and O(logn) maximum degree. This is asymptotically the best possible.
Our algorithms are based on the following result, which is a non-trivial consequence of classical percolation theory: suppose that all devices set up their transmission radius in order to reach the K closest devices. There exists a universal constant K (independent of n) such that, with high probability, there will be a unique giant component, i.e. a connected component of size Θ(n). Furthermore, all remaining components will be of size O(log2 n). This leads to an efficient distributed probabilistic test for membership in the giant component, which can be used in a second phase to achieve full connectivity.
Preliminary experiments suggest that our approach might very well lead to efficient protocols in real wireless applications.
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
Blough, D., Leoncini, M., Resta, G., Santi, P.: The k-Neighbors Approach to Interference Bounded and Symmetric Topology Control in Ad Hoc Networks, IEEE Trans. on Mobile Computing
Deuschel, J.-D., Pisztora, A.: Surface order large deviations for high-density percolation. Probability Theory and Related Fields 104(4), 467–482 (1996)
Grimmet, G.: Percolation. Springer, Heidelberg (1989)
Häggström, O., Meester, R.: Nearest neighbor and hard sphere models in continuum percolation. Random Structures and Algorithms 9, 295–315 (1996)
Hou, T., Li, V.: Transmission range control in multihop packet radio networks. IEEE Transactions on Communications COM-34, 38–44 (1986)
Kleinrock, L., Silvester, J.: Optimum transmission radii for packet radio networks or why six is a magic number. In: IEEE National Telecommunication Conference, pp. 431–435 (1978)
Kucera, L.: Low degree connectivity in ad-hoc networks. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 203–214. Springer, Heidelberg (2005)
Liggett, T.M., Schonmann, R.H., Stacey, A.M.: Domination by product measures. Annals of Probability 25(1), 71–95 (1997)
Meester, R., Roy, R.: Continuum Percolation. Cambridge University Press, Cambridge (1996)
Ni, J., Chandler, S.A.G.: Connectivity Properties of a Random Radio Network. IEE Prec. Commun. 141, 289–296 (1994)
Takagi, H., Kleinrock, L.: Optimal transmission ranges for randomly distributed packet radio terminals. IEEE Transactions on Communications COM-32(3), 246–257 (1984)
Xue, F., Kumar, P.: The number of neighbors needed for connectivity of wireless networks. Wireless Networks 10(2), 169–181 (2004)
Zhu, S., Setia, S., Jajodia, S.: LEAP: Efficient Security Mechanisms for Large-Scale Distributed Sensor Networks. In: Proc. of the 10th ACM Conference on Computer and Communications Security (CCS 2003), Washington, D.C. (October 2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
De Santis, E., Grandoni, F., Panconesi, A. (2007). Fast Low Degree Connectivity of Ad-Hoc Networks Via Percolation. In: Arge, L., Hoffmann, M., Welzl, E. (eds) Algorithms – ESA 2007. ESA 2007. Lecture Notes in Computer Science, vol 4698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75520-3_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-75520-3_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75519-7
Online ISBN: 978-3-540-75520-3
eBook Packages: Computer ScienceComputer Science (R0)