Abstract
We introduce a general model for online packing problems with applications to lifetime optimization of wireless sensor networks. Classical approaches for lifetime maximization make the crucial assumption that battery capacities of sensor nodes are known a priori. For real-world batteries, however, the capacities are only vaguely known. To capture this aspect, we introduce an adversarial online model where estimates become more and more accurate over time, that is, when using the corresponding resources. Our model is based on general linear packing programs and we assume the remaining capacities to be always specified by lower and upper bounds that may deviate from each other by a fixed factor α.
We analyze the algorithmic consequences of our model and provide a general -competitive framework. Furthermore, we show a complementary upper bound of .
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References
Awerbuch, B., Azar, Y., Plotkin, S.A.: Throughput-competitive on-line routing. In: FOCS, pp. 32–40 (1993)
Azar, Y., Feige, U., Glasner, D.: A preemptive algorithm for maximizing disjoint paths on trees. Algorithmica 57(3), 517–537 (2010)
Bienstock, D., Iyengar, G.: Approximating fractional packings and coverings in o(1/epsilon) iterations. SIAM J. Comput. 35(4), 825–854 (2006)
Birge, J., Louveaux, F.: Introduction to stochastic programming. Springer (1997)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press (1998)
Buchbinder, N., Naor, J.: Online primal-dual algorithms for covering and packing. Math. Oper. Res. 34(2), 270–286 (2009)
Calinescu, G., Kapoor, S., Olshevsky, A., Zelikovsky, A.: Network Lifetime and Power Assignment in ad hoc Wireless Networks. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 114–126. Springer, Heidelberg (2003)
Elkin, M., Lando, Y., Nutov, Z., Segal, M., Shpungin, H.: Novel algorithms for the network lifetime problem in wireless settings. Wireless Netw. 17, 397–410 (2011)
Gabow, H.N., Manu, K.S.: Packing algorithms for arborescences (and spanning trees) in capacitated graphs. Math. Program. 82, 83–109 (1998)
Garg, N., Gupta, A., Leonardi, S., Sankowski, P.: Stochastic analyses for online combinatorial optimization problems. In: SODA, pp. 942–951 (2008)
Garg, N., Könemann, J.: Faster and simpler algorithms for multicommodity flow and other fractional packing problems. In: FOCS, pp. 300–309 (1998)
Immorlica, N., Karger, D.R., Minkoff, M., Mirrokni, V.S.: On the costs and benefits of procrastination: approximation algorithms for stochastic combinatorial optimization problems. In: SODA, pp. 691–700 (2004)
Karp, R.M., Nierhoff, T., Tantau, T.: Optimal Flow Distribution Among Multiple Channels with Unknown Capacities. In: Goldreich, O., Rosenberg, A.L., Selman, A.L. (eds.) Theoretical Computer Science. LNCS, vol. 3895, pp. 111–128. Springer, Heidelberg (2006)
Michael, S.: Fast algorithm for multicast and data gathering in wireless networks. Information Processing Letters 107(1), 29–33 (2008)
Orda, A., Yassour, B.A.: Maximum-lifetime routing algorithms for networks with omnidirectional and directional antennas. In: MobiHoc, pp. 426–437 (2005)
Park, J., Sahni, S.: Maximum lifetime broadcasting in wireless networks. IEEE Transactions on Computers 54(9), 1081–1090 (2005)
Plotkin, S.A., Shmoys, D.B., Tardos, É.: Fast approximation algorithms for fractional packing and covering problems. In: FOCS, pp. 495–504 (1991)
Rao, R., Vrudhula, S., Rakhmatov, D.: Battery modeling for energy aware system design. Computer 36(12), 77–87 (2003)
Shmoys, D.B., Swamy, C.: Stochastic optimization is (almost) as easy as deterministic optimization. In: FOCS, pp. 228–237 (2004)
Srinivasan, A.: Approximation algorithms via randomized rounding: A survey. Series in Advanced Topics in Mathematics, pp. 9–71. Polish Scientific Publishers PWN (1999)
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Ochel, M., Radke, K., Vöcking, B. (2012). Online Packing with Gradually Improving Capacity Estimations and Applications to Network Lifetime Maximization. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31585-5_57
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DOI: https://doi.org/10.1007/978-3-642-31585-5_57
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