Abstract
In the relay placement problem the input is a set of sensors and a number r ≥ 1, the communication range of a relay. The objective is to place a minimum number of relays so that between every pair of sensors there is a path through sensors and/or relays such that the consecutive vertices of the path are within distance r if both vertices are relays and within distance 1 otherwise. We present a 3.11-approximation algorithm, and show that the problem admits no PTAS, assuming P\({}\ne{}\)NP.
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References
Chen, D., Du, D.Z., Hu, X.D., Lin, G.H., Wang, L., Xue, G.: Approximations for Steiner trees with minimum number of Steiner points. Journal of Global Optimization 18(1), 17–33 (2000)
Chen, D., Du, D.Z., Hu, X.D., Lin, G.H., Wang, L., Xue, G.: Approximations for Steiner trees with minimum number of Steiner points. Theoretical Computer Science 262(1–2), 83–99 (2001)
Cheng, X., Du, D.Z., Wang, L., Xu, B.: Relay sensor placement in wireless sensor networks. Wireless Networks (to appear, 2007)
Liu, H., Wan, P.J., Jia, X.: Fault-tolerant relay node placement in wireless sensor networks. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 230–239. Springer, Heidelberg (2005)
Lloyd, E.L., Xue, G.: Relay node placement in wireless sensor networks. IEEE Transactions on Computers 56(1), 134–138 (2007)
Srinivas, A., Zussman, G., Modiano, E.: Mobile backbone networks – construction and maintenance. In: Proc. 7th ACM International Symposium on Mobile Ad Hoc Networking and Computing, MobiHoc, Florence, Italy, May 2006, pp. 166–177. ACM Press, New York (2006)
Zhang, W., Xue, G., Misra, S.: Fault-tolerant relay node placement in wireless sensor networks: Problems and algorithms. In: Proc. 26th IEEE International Conference on Computer Communications, INFOCOM, Anchorage, Alaska, USA, May 2007, pp. 1649–1657. IEEE, Piscataway (2007)
Bredin, J.L., Demaine, E.D., Hajiaghayi, M., Rus, D.: Deploying sensor networks with guaranteed capacity and fault tolerance. In: Proc. 6th ACM International Symposium on Mobile Ad Hoc Networking and Computing, MobiHoc, Urbana-Champaign, IL, USA, May 2005, pp. 309–319. ACM Press, New York (2005)
Cerdeira, J.O., Pinto, L.S.: Requiring connectivity in the set covering problem. Journal of Combinatorial Optimization 9(1), 35–47 (2005)
Shuai, T.P., Hu, X.D.: Connected set cover problem and its applications. In: Cheng, S.-W., Poon, C.K. (eds.) AAIM 2006. LNCS, vol. 4041, pp. 243–254. Springer, Heidelberg (2006)
Yang, Y., Lin, M., Xu, J., Xie, Y.: Minimum spanning tree with neighborhoods. In: Kao, M.-Y., Li, X.-Y. (eds.) AAIM 2007. LNCS, vol. 4508, pp. 306–316. Springer, Heidelberg (2007)
Du, D.Z., Hwang, F.: An approach for proving lower bounds: Solution of Gilbert–Pollak’s conjecture on Steiner ratio. In: Proc. 31st Annual Symposium on Foundations of Computer Science, FOCS, St. Louis, MO, USA, October 1990, pp. 76–85. IEEE, Piscataway (1990)
Berman, P., Karpinski, M.: On some tighter inapproximability results. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 200–209. Springer, Heidelberg (1999)
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Efrat, A., Fekete, S.P., Gaddehosur, P.R., Mitchell, J.S.B., Polishchuk, V., Suomela, J. (2008). Improved Approximation Algorithms for Relay Placement. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_30
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DOI: https://doi.org/10.1007/978-3-540-87744-8_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87743-1
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