Abstract
Assumptions about node density in the Sensor Networks literature are frequently too strong or too weak. Neither absolutely arbitrary nor uniform deployment seem feasible in most of the intended applications of sensor nodes. We present a Weak Sensor Model-compatible distributed protocol for hop-optimal network initialization, under the assumption that the maximum density of nodes is some value Δ known by all of the nodes. In order to prove lower bounds, we observe that all nodes must communicate with some other node in order to join the network, and we call the problem of achieving such a communication the Group Therapy Problem. We show lower bounds for the Group Therapy Problem in Radio Networks of maximum density Δ, regardless of the use of randomization, and a stronger lower bound for the important class of randomized fair protocols. We also show that even when nodes are distributed uniformly, the same lower bound holds, even in expectation and even for the simpler problem of Clear Transmission.
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
Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., Cyirci, E.: Wireless sensor networks: A survey. Computer Networks 38(4), 393–422 (2002)
Bar-Yehuda, R., Goldreich, O., Itai, A.: On the time-complexity of broadcast in multi-hop radio networks: An exponential gap between determinism and randomization. Journal of Computer and System Sciences 45, 104–126 (1992)
Blough, D.M., Leoncini, M., Resta, G., Santi, P.: The k-neigh protocol for symmetric topology control in ad hoc networks. In: Proc. of the 4th ACM international symposium on Mobile ad hoc networking and computing, pp. 141–152 (2003)
Chlebus, B., Ga̧sieniec, L., Lingas, A., Pagourtzis, A.: Oblivious gossiping in ad-hoc radio networks. In: Proc. of 5th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, pp. 44–51 (2001)
Farach-Colton, M., Fernandes, R.J., Mosteiro, M.A.: Bootstrapping a hop-optimal network in the weak sensor model. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 827–838. Springer, Heidelberg (2005)
Farach-Colton, M., Fernandes, R.J., Mosteiro, M.A.: Lower bounds for clear transmissions in radio networks. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 447–454. Springer, Heidelberg (2006)
Gerèb-Graus, M., Tsantilas, T.: Efficient optical communication in parallel computers. In: 4th Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 41–48 (1992)
Jurdziński, T., Stachowiak, G.: Probabilistic algorithms for the wakeup problem in single-hop radio networks. Theory of Computing Systems 38(3), 347–367 (2005)
Karl, H., Willig, A.: A short survey of wireless networks. Technical Report TKN-03-018, Technical University Berlin (October 2003)
Kowalski, D.R.: On selection problem in radio networks. In: Proceedings 24th Annual ACM Symposium on Principles of Distributed Computing, pp. 158–166 (2005)
Kumar, V.S.A., Marathe, M.V., Parthasarathy, S., Srinivasan, A.: End-to-end packet-scheduling in wireless ad-hoc networks. In: Proc. of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1021–1030 (2004)
Kushilevitz, E., Mansour, Y.: An Ω(Dlog(N/D)) lower bound for broadcast in radio networks. SIAM Journal on Computing 27(3), 702–712 (1998)
Liu, D., Prabhakaran, M.: On randomized broadcasting and gossiping in radio networks. In: Ibarra, O.H., Zhang, L. (eds.) COCOON 2002. LNCS, vol. 2387, pp. 340–349. Springer, Heidelberg (2002)
Martel, C.U.: Maximum finding on a multiple access broadcast network. Inf. Process. Lett. 52, 7–13 (1994)
Mitrinović, D.S.: Elementary Inequalities. P. Noordhoff Ltd. - Groningen (1964)
Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)
Muthukrishnan, S., Pandurangan, G.: The bin-covering technique for thresholding random geometric graph properties. In: Proc. of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 989–998 (2005)
Nakano, K., Olariu, S.: Energy-efficient initialization protocols for radio networks with no collision detection. In: ICPP, pp. 263–270 (2000)
Ponduru, V.A.S., Bharathidasan, A.: Sensor networks: An overview. Technical report, University of California, Davis (2003)
Rentala, P., Musumuri, R., Saxena, U., Gandham, S.: Survey on sensor networks. http://citeseer.nj.nec.com/479874.html
Sohrabi, K., Gao, J., Ailawadhi, V., Pottie, G.J.: Protocols for self-organization of a wireless sensor network. Personal Communications, IEEE 7(5), 16–27 (2000)
Song, W., Wang, Y., Li, X., Frieder, O.: Localized algorithms for energy efficient topology in wireless ad hoc networks. In: Proc. of the 5th ACM international symposium on Mobile ad hoc networking and computing, pp. 98–108 (2004)
Younis, O., Krunz, M., Ramasubramanian, S.: Node clustering in wireless sensor networks: Recent developments and deployment challenges. IEEE Network Magazine 20, 20–25 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Farach-Colton, M., Mosteiro, M.A. (2007). Initializing Sensor Networks of Non-uniform Density in the Weak Sensor Model. In: Dehne, F., Sack, JR., Zeh, N. (eds) Algorithms and Data Structures. WADS 2007. Lecture Notes in Computer Science, vol 4619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73951-7_49
Download citation
DOI: https://doi.org/10.1007/978-3-540-73951-7_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73948-7
Online ISBN: 978-3-540-73951-7
eBook Packages: Computer ScienceComputer Science (R0)