Abstract
A sensor with two active phrases means that active mode has two phases, the full-active phase and the semi-active phase, which require different energy consumptions. A full-active sensor can sense data packets, transmit, receive, and relay the data packets. A semi-active sensor cannot sense data packets, but it can transmit, receive, and relay data packets. Given a set of targets and a set of sensors with two active phrases, find a sleep/active schedule of sensors to maximize the time period during which active sensors form a connected coverage set. In this paper, this problem is showed to have polynomial-time \({(7.875+\varepsilon)}\)-approximations for any \({\varepsilon >0 }\) when all targets and sensors lie in the Euclidean plane and all sensors have the same sensing radius R s and the same communication radius R c with R c ≥ 2R s .
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References
Ambühl, C., Erlebach, T., Mihalák, M., Nunkesser, M.: Constant-approximation for minimum-weight (connected) dominating sets in unit disk graphs. In: Proceedings of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX 2006), LNCS 4110, Springer, pp. 3–14 (2006)
Baker, B.S.: Approximation algorithms for NP-complete problems on planar graphs. In: Proceedings of the FOCS, pp. 265–273 (1983)
Boginski, V.L., Commander, C.W., Pardalos, P.M., Ye, Y. (eds): Sensors: Theory, Algorithms, and Applications. Springer, Berlin (2012)
Du D.-Z., Ko K.-I., Hu X.: Design and Analysis of Approximation Algorithms, pp. 142–157. Springer, Berlin (2012)
Du H., Wu W., Shan S., Kim D., Lee W.: Constructing weakly connected dominating set for secure clustering in distributed sensor network. J. Comb. Optim. 23, 301–307 (2012)
Erlebach, T., Mihalk, M.: A \({(4 + \epsilon)}\)-approximation for the minimum-weight dominating set problem in unit disk graphs. WAOA, pp. 135–146 (2009)
Garg, N., Könemann, J.: Faster and simpler algorithms for multicommodity flows and other fractional packing problems. In: Proceedings of the 39th Annual Symposium on the Foundations of Computer Science, pp. 300–309 (1998)
Hochbaum D.S., Maass W.: Approximation schemes for covering and packing problems in image processing and VLSI. J. ACM 32, 130–136 (1985)
Huang Y., Gao X., Zhang Z., Wu W.: A better constant-factor approximation for weighted dominating set in unit disk graph. J. Comb. Optim. 18, 174–194 (2009)
Sorokin A., Boyko N., Boginski V., Uryasev S., Pardalos P.: Mathematical programming techniques for sensor networks. Algorithms 2, 565–581 (2009)
Wang C., Willson J., Park M.A., Farago A., Wu W.: On dual power assignment optimization for biconnectivity. J. Comb. Optim. 19, 174–183 (2010)
Wu W., Gao X., Pardalos P.M., Du D.-Z.: Wireless networking, dominating and packing. Optim. Lett. 4, 347–358 (2010)
Yang Y., Cardei M.: Adaptive energy efficient sensor scheduling for wireless sensor networks. Optim. lett. 4(3), 359–369 (2010)
Zhang H., Hou J.C.: Maintaining sensing coverage and connectivity in large sensor networks. Ad Hoc Sens. Wirel. Netw. 1, 89–124 (2005)
Zhang, Y., Li, W.: Modeling and energy consumption evaluation of a stochastic wireless sensor networks. (2011, preprint)
Zou F., Li X., Gao S., Wu W.: Node-weighted Steiner tree approximation in unit disk graphs. J. Comb. Optim. 18, 342–349 (2009)
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Du, H., Pardalos, P.M., Wu, W. et al. Maximum lifetime connected coverage with two active-phase sensors. J Glob Optim 56, 559–568 (2013). https://doi.org/10.1007/s10898-012-9871-x
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DOI: https://doi.org/10.1007/s10898-012-9871-x