Abstract
Topology control is the problem of assigning transmission power values to the nodes of an ad hoc network so that the induced graph satisfies some specified property. The most fundamental such property is that the network/graph be connected. For connectivity, prior work on topology control gave a polynomial time algorithm for minimizing the maximum power assigned to any node (such that the induced graph is connected). In this paper we study the problem of minimizing the number of maximum power nodes. After establishing that this minimization problem is NP-Complete, we focus on approximation algorithms for graphs with symmetric power thresholds. We first show that the problem is reducible in an approximation preserving manner to the problem of assigning power values so that the sum of the powers is minimized. Using known results for that problem, this provides a family of approximation algorithms for the problem of minimizing the number of maximum power nodes with approximation ratios of 5/3 + ε for every ε > 0. Unfortunately, these algorithms, based on solving large linear programming problems are not practical. The main result of this paper is a practical algorithm having a 5/3 (exactly) approximation ratio. In addition, we present experimental results on randomly generated networks. Finally, based on the reduction to minimizing the total power problem, we outline some additional results for minimizing the number of maximum power users, both for graph properties other than connectivity and for graphs with asymmetric power thresholds.
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
Althaus, E., Calinescu, G., Mandoiu, I., Prasad, S., Tchervenski, N., Zelikovksy, A.: Power Efficient Range Assignment for Symmetric Connectivity in Static Ad Hoc Wireless Networks. Private communication
Chen, W., Huang, N.: The Strongly Connecting Problem on Multihop Packet Radio Networks. IEEE Trans. Communication 37(3), 293–295 (1989)
Clementi, A.E.F., Penna, P., Silvestri, R.: Hardness results for the power range assignment problem in packet radio networks. In: Hochbaum, D.S., Jansen, K., Rolim, J.D.P., Sinclair, A. (eds.) RANDOM 1999 and APPROX 1999. LNCS, vol. 1671, pp. 197–208. Springer, Heidelberg (1999)
Clementi, A.E.F., Penna, P., Silvestri, R.: The Power Range Assignment Problem in Packet Radio Networks in the Plane. In: Proc. 17th Annual Symposium on Theoretical Aspects of Computer Science (STACS 2000), February 2000, pp. 651–660 (2000)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman and Co, San Francisco (1979)
Guha, S., Khuller, S.: Improved Methods for Approximating Node Weighted Steiner Trees and Connected Dominating Sets. Information and Computation 150, 57–74 (1999)
Kirousis, L.M., Kranakis, E., Krizanc, D., Pelc, A.: Power Consumption in Packet Radio Networks. In: Reischuk, R., Morvan, M. (eds.) STACS 1997. LNCS, vol. 1200, pp. 363–374. Springer, Heidelberg (1997)
Krumke, S.O., Liu, R., Lloyd, E.L., Marathe, M.V., Ramanathan, R., Ravi, S.S.: Topology Control Problems Under Symmetric and Asymmetric Power Thresholds. In: Pierre, S., Barbeau, M., Kranakis, E. (eds.) ADHOC-NOW 2003. LNCS, vol. 2865, pp. 187–198. Springer, Heidelberg (2003)
Lloyd, E., Liu, R., Marathe, M., Ramanathan, R., Ravi, S.S.: Algorithmic Aspects of Topology Control Problems for Ad hoc Networks. In: Proc. Third ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc), pp. 123–134 (2002) (Complete version to appear in Mobile Networks and Applications)
Li, L., Halpern, J.Y., Bahl, P., Wang, Y., Wattenhofer, R.: Analysis of Cone-Based Distributed Topology Control Algorithm for Wireless Multihop Networks. In: Proc. ACM Principles of Distributed Computing Conference (PODC 2001), August 2001, pp. 264–273 (2001)
Rappaport, T.S.: Wireless Communications: Principles and Practice. Prentice-Hall, Inc., Englewood Cliffs (1996)
Radoplu, V., Meng, T.H.: Minimum Energy Mobile Wireless Networks. IEEE J. Selected Areas in Communications 17(8), 1333–1344 (1999)
Royer, E.M., Melliar-Smith, P., Moser, L.: An Analysis of the Optimum Node Density for Ad hoc Mobile Networks. In: Proc. IEEE Intl. Conf. on Communication (ICC 2001), Helsinki, Finland, June 2001, pp. 857–861 (2001)
Ramanathan, R., Rosales-Hain, R.: Topology Control of Multihop Wireless Networks Using Transmit Power Adjustment. In: Proc. IEEE INFOCOM 2000, Tel Aviv, Israel, March 2000, pp. 404–413 (2000)
Wattenhofer, R., Li, L., Bahl, P., Wang, Y.: Distributed Topology Control for Power Efficient Operation in Multihop Wireless Ad Hoc Networks. In: Proc. IEEE INFOCOM 2001, Anchorage, Alaska, April 2001, pp. 1388–1397 (2001)
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
Lloyd, E.L., Liu, R., Ravi, S.S. (2004). Approximating the Minimum Number of Maximum Power Users in Ad Hoc Networks. In: Nikolaidis, I., Barbeau, M., Kranakis, E. (eds) Ad-Hoc, Mobile, and Wireless Networks. ADHOC-NOW 2004. Lecture Notes in Computer Science, vol 3158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28634-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-28634-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22543-0
Online ISBN: 978-3-540-28634-9
eBook Packages: Springer Book Archive