Abstract
Given a set S of n pre-placed radio-stations and a source station s *, we consider two variations of minimum cost homogeneous range assignment problem for the 2-hops broadcast from s * to all the members in S, where the range assigned to a radio-station is either zero or a fixed value r. Thus, the cost of range assignment is proportional to the number of radio-stations having range r. The variations we study are (i) find the value of r and identify the radio-stations with range r such that the total cost is minimum, and (ii) given a real number r, check whether homogeneous 2-hops broadcast from s * to the members in S is possible with range r, and if so, then identify the smallest subset of S whom range r is to be assigned such that 2-hops broadcast from s * is possible. The first problem is solved in O(n 3) time and space. But, the second one seems to be hard. We present a 3-factor approximation algorithm for this problem, which runs in O(n 2) time. An O(n 2) time heuristic algorithm for the second problem is also presented. Most of the times, it produces optimum result for randomly placed radio-stations.
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Ambuhl, C., Clementi, A.E.F., Di Ianni, M., Lev-Tov, N., Monti, A., Peleg, D., Rossi, G., Silvestri, R.: Efficient Algorithms for Low-Energy Bounded-Hop Broadcast in Ad-Hoc Wireless Networks. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 418–427. Springer, Heidelberg (2004)
Cagalj, M., Hubaux, J.-P., Enz, C.: Minimum energy broadcast in all wireless networks: NP-completeness and distribution issues. In: Proc. of the 8th. Annual Int. Conf. on Mobile Computing and Networking, pp. 172–182 (2002)
Clementi, A.E.F., Huiban, G., Penna, P., Rossi, G., Verhoeven, Y.C.: Some recent theoretical advances and open questions on energy consumption in Ad Hoc wireless networks. In: Proc. 3rd. Workshop on Approximation and Randomization Algorithms in Communication Networks, pp. 23–38 (2002)
Clementi, A.E.F., Di Ianni, M., Silvestri, R.: The minimum broadcast range assignment problem on linear multihop wireless networks. Theoretical Computer Science 299, 751–761 (2003)
Das, G.K., Das, S., Nandy, S.C.: Efficient Algorithm for Energy Efficient Broadcasting in Linear Radio Networks. Theoretical Computer Science 352, 332–341 (2006)
Haas, Z.J., Tabrizi, S.: On some challenges and design choices in ad-hoc communications. In: Proc. IEEE military communication conference (MILCOM 1998), vol. 1, pp. 187–192 (1998)
Pahlavan, K., Levesque, A.: Wireless information networks. John Wiley, New York (1995)
Park, J., Sahni, S.: Maximum lifetime broadcasting in wireless networks. IEEE Trans. on Computers 54, 1081–1090 (2005)
Santi, P.: Topology Control in Wireless Ad Hoc and Sensor Networks. John Wiley & Sons, Chichester (2005)
Wan, P.-J., Calinescu, G., Li, X.-Y., Frieder, O.: Minimum energy broadcast in static ad hoc wireless networks. Wireless Networks 8, 607–617 (2002)
Zosin, L., Khuller, S.: On directed Steiner trees. In: Proc. 13th. Annual ACM-SIAM symposium on Discrete algorithms (SODA 2002), pp. 59–63 (2002)
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Das, G.K., Das, S., Nandy, S.C. (2006). Homogeneous 2-Hops Broadcast in 2D. In: Gavrilova, M.L., et al. Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11751588_78
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DOI: https://doi.org/10.1007/11751588_78
Publisher Name: Springer, Berlin, Heidelberg
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