Homogeneous 2-Hops Broadcast in 2D
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.
KeywordsWireless Network Time Complexity Approximation Algorithm Steiner Tree Multihop Wireless Network
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- 1.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)CrossRefGoogle Scholar
- 2.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)Google Scholar
- 3.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)Google Scholar
- 6.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)Google Scholar
- 7.Pahlavan, K., Levesque, A.: Wireless information networks. John Wiley, New York (1995)Google Scholar
- 11.Zosin, L., Khuller, S.: On directed Steiner trees. In: Proc. 13th. Annual ACM-SIAM symposium on Discrete algorithms (SODA 2002), pp. 59–63 (2002)Google Scholar