The Community for Technology Leaders
RSS Icon
Issue No.02 - February (2011 vol.22)
pp: 208-216
Tiziana Calamoneri , Sapienza Università di Roma, Roma
Andrea E.F. Clementi , Università degli studi di Roma Tor Vergata, Roma
Emanuele G. Fusco , Sapienza Università di Roma, Roma
Riccardo Silvestri , Sapienza Università di Roma, Roma
We consider static ad hoc wireless networks whose nodes, equipped with the same initial battery charge, may dynamically change their transmission range. When a node v transmits with range r(v), its battery charge is decreased by \beta r(v)^2, where \beta >0 is a fixed constant. The goal is to provide a range assignment schedule that maximizes the number of broadcast operations from a given source (this number is denoted by the length of the schedule). This maximization problem, denoted by Max LifeTime, is known to be NP-hard and the best algorithm yields worst-case approximation ratio \Theta (\log n), where n is the number of nodes of the network. We consider random geometric instances formed by selecting n points independently and uniformly at random from a square of side length \sqrt{n} in the euclidean plane. We present an efficient algorithm that constructs a range assignment schedule having length not smaller than 1/12 of the optimum with high probability. Then we design an efficient distributed version of the above algorithm, where nodes initially know n and their own position only. The resulting schedule guarantees the same approximation ratio achieved by the centralized version, thus, obtaining the first distributed algorithm having provably good performance for this problem.
Energy-aware systems, wireless communication, graph algorithms, network problems.
Tiziana Calamoneri, Andrea E.F. Clementi, Emanuele G. Fusco, Riccardo Silvestri, "Maximizing the Number of Broadcast Operations in Random Geometric Ad Hoc Wireless Networks", IEEE Transactions on Parallel & Distributed Systems, vol.22, no. 2, pp. 208-216, February 2011, doi:10.1109/TPDS.2010.77
[1] C. Ambuehl, "An Optimal Bound for the MST Algorithm to Compute Energy Efficient Broadcast Trees in Wireless Networks," Proc. Int'l Colloquium Automata, Languages and Programming (ICALP '05), pp. 1139-1150, 2005.
[2] R. Bar-Yehuda, O. Goldreich, and A. Itai, "On the Time-Complexity of Broadcast in Multi-Hop Radio Networks: An Exponential Gap between Determinism and Randomization," J. Computer and System Sciences (JCSS), vol. 45, pp. 104-126, 1992.
[3] R. Bar-Yehuda, A. Israeli, and A. Itai, "Multiple Communication in Multi-Hop Radio Networks," SIAM J. Computing (SICOMP), vol. 22, no. 4, pp. 875-887, 1993.
[4] G. Calinescu, X.Y. Li, O. Frieder, and P.J. Wan, "Minimum-Energy Broadcast Routing in Static Ad Hoc Wireless Networks," Proc. IEEE INFOCOM, pp. 1162-1171, Apr. 2001.
[5] G. Calinescu, S. Kapoor, A. Olshevsky, and A. Zelikovsky, "Network Lifetime and Power Assignment in Ad Hoc Wireless Networks," Proc. European Symp. Algorithms (ESA '03), pp. 114-126, 2003.
[6] I. Caragiannis, M. Flammini, and L. Moscardelli, "An Exponential Improvement on the MST Heuristic for the Minimum Energy Broadcast Problem," Proc. Int'l Colloquium Automata, Languages and Programming (ICALP '07), pp. 447-458, 2007.
[7] M. Cardei and D.Z. Du, "Improving Wireless Sensor Network Lifetime through Power Organization," Wireless Networks, vol. 11, pp. 333-340, 2005.
[8] M. Cardei, J. Wu, and M. Lu, "Improving Network Lifetime Using Sensors with Adjustable Sensing Ranges," Int'l J. Sensor Networks, vol. 1, nos. 1/2, pp. 41-49, 2006.
[9] T. Calamoneri, A. Clementi, A. Monti, G. Rossi, and R. Silvestri, "Minimum-Energy Broadcast in Random-Grid Ad-Hoc Networks: Approximation and Distributed Algorithms," Proc. 11th ACM Int'l Symp. Modeling, Analysis and Simulation of Wireless and Mobile Systems (MSWiM), 2008.
[10] A. Clementi, P. Crescenzi, P. Penna, G. Rossi, and P. Vocca, "On the Complexity of Computing Minimum Energy Consumption Broadcast Subgraphs," Proc. 18th Ann. Symp. Theoretical Aspects of Computer Science (STACS), pp. 121-131,, Feb. 2001.
[11] A. Clementi, G. Huiban, P. Penna, G. Rossi, and Y.C. Verhoeven, "On the Approximation Ratio of the MST-Based Heuristic for the Energy-Efficient Broadcast Problem in Static Ad-Hoc Radio Networks," Proc. Int'l Parallel and Distributed Processing Symp. (IPDPS '03), vol. 222, 2003.
[12] A.E.F. Clementi, A. Monti, and R. Silvestri, "Distributed Broadcast in Radio Networks of Unknown Topology," Theoretical Computer Science, vol. 302, nos. 1-3, pp. 337-364, 2003.
[13] M. Chrobak, L. Gasieniec, and W. Rytter, "Fast Broadcasting and Gossiping in Radio Networks," J. Algorithms, vol. 43, no. 2, pp. 177-189, 2002.
[14] W. Chu, C.J. Colbourn, and V.R. Syrotiuk, "The Effects of Synchronization on Topology Transparent Scheduling," Wireless Networks, vol. 12, pp. 681-690, 2006.
[15] A. Czumaj and W. Rytter, "Broadcasting Algorithms in Radio Networks with Unknown Topology," J. Algorithms, vol. 60, no. 2, pp. 115-143, 2006.
[16] A. Dessmark and A. Pelc, "Broadcasting in Geometric Radio Networks," J. Discrete Algorithms, vol. 5, no. 1, pp. 187-201, 2007.
[17] A. Ephremides, G.D. Nguyen, and J.E. Wieselthier, "On the Construction of Energy-Efficient Broadcast and Multicast Trees in Wireless Networks," Proc. IEEE INFOCOM, pp. 585-594, 2000.
[18] A.D. Flaxman, A.M. Frieze, and J.C. Vera, "On the Average Case Performance of Some Greedy Approximation Algorithms for the Uncapacitated Facility Location Problem," Proc. ACM Symp. Theory of Computing (STOC '05), pp. 441-449, 2005.
[19] M. Flammini, A. Navarra, and S. Perennes, "The Real Approximation Factor of the MST Heuristic for the Minimum Energy Broadcast," Proc. Int'l Workshop Experimental and Efficient Algorithms (WEA '05), pp. 22-31, 2005.
[20] P. Gupta and P.R. Kumar, "Critical Power for Asymptotic Connectivity in Wireless Networks," Stochastic Analysis, Control, Optimization and Applications, pp. 547-566, Birkhauser, 1999.
[21] I. Kang and R. Poovendran, "Maximizing Network Lifetime of Wireless Broadcast Ad Hoc Networks," J. ACM Mobile Networks and Applications, vol. 10, no. 6, pp. 879-896, 2005.
[22] L.M. Kirousis, E. Kranakis, D. Krizanc, and A. Pelc, "Power Consumption in Packet Radio Networks," Theoretical Computer Science, vol. 243, pp. 289-305, 2000.
[23] M. Mitzenmacher and E. Upfal, Probability and Computing. Cambridge Univ. Press, 2005.
[24] K. Pahlavan and A. Levesque, Wireless Information Networks. Wiley-Interscience, 1995.
[25] M. Penrose, Random Geometric Graphs. Oxford Univ. Press, 2003.
[26] P. Santi and D.M. Blough, "The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks," IEEE Trans. Mobile Computing, vol. 2, no. 1, pp. 25-39, Jan.-Mar. 2003.
532 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool