Abstract
This article addresses a real-life problem - obtaining communication links between multiple base station sites, by positioning a minimal set of fixed-access relay antenna sites on a given terrain. Reducing the number of relay antenna sites is considered critical due to substantial installation and maintenance costs. Despite the significant cost saved by eliminating even a single antenna site, an inefficient manual approach is employed due to the computational complexity of the problem. From the theoretical point of view we show that this problem is not only NP hard, but also does not have a constant approximation. In this paper we suggest several alternative automated heuristics, relying on terrain preprocessing to find educated potential points for positioning relay stations. A large-scale computer-based experiment consisting of approximately 7,000 different scenarios was conducted. The quality of alternative solutions was compared by isolating and displaying factors that were found to affect the standard deviation of the solutions supplied by the tested heuristics. The results of the simulation based experiments show that the saving potential increases when more base stations are needed to be interconnected. The designs of a human expert were compared to the automatically generated solutions for a small subset of the experiment scenarios. Our studies indicate that for small networks (e.g., connecting up to ten base stations), the results obtained by human experts are adequate although they rarely exceed the quality of automated alternatives. However, the process of obtaining these results in comparison to automated heuristics is longer. In addition, when more base station sites need to be interconnected, the human approach is easily outperformed by our heuristics, both in terms of better results (fewer antennas) and in significant shorter calculation times.
Similar content being viewed by others
References
Agrawal, P.K., Har-Peled, S., Sharir, M., Varadarajan, K.R.: Approximate shortest paths on a convex polytope in three dimensions. J. ACM 44, 567–584 (1997)
Anderson, H.R., McGeehan, J.P.: Optimizing microcell base station locations using simulated annealing techniques. In: Proc. of the IEEE Vehicular Technology Conference, pp. 858–862 (1994)
Available at http://www.alvarion.com/
Available at http://www.hexagonltd.com/
Available at http://www.schema.com/
Ben-Moshe, B.: Geometric facility location optimization, Ph.D. Thesis, Ben-Gurion University of the Negev (2004)
Berman, P., Ramaiyer, V.: Improved approximations for the Steiner tree problem. J. Algorithms 17, 381–408 (1994)
Blaunstein, N.: Radio Propagation in Cellular Networks. Artech House, Boston (1999)
Calgeri, P., Kuonen, P., Nielsen, F.: Combinatorial optimization algorithms for radio network planning. Theor. Comput. Sci. 263, 235–245 (2001)
Efroymson, M.A., Ray, T.L.: A branch and bound algorithm for plant location. Oper. Res. 14, 361–368 (1966)
Feige, U.: A threshold of ln n for approximating set cover (preliminary version). In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 314–318 (1996)
Hao, J.K., Dorne, R., Galinier, P.: Tabu search for frequency assignment in mobile radio networks. J. Heuristics 4, 47–62 (1998)
Har-Peled, S.: Constructing approximate shortest path maps in three dimensions. SIAM J. Comput. 28, 1187–1197 (1999)
Hougardy, S., Prömel, H.J.: A 1.598 approximation algorithm for the Steiner problem in graphs. In: Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 448–453 (1999)
Hwang, F.K., Richards, D.S., Winter, P.: The Steiner Tree Problem. Elsevier, Amsterdam (1992)
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum, New York (1972)
Karpinsky, M., Zelikovsky, A.: New approximation algorithms for the Steiner tree problem. J. Comb. Optim. 1, 47–65 (1997)
Mitchell, J.S., Geometric Shortest Paths and Network Optimization. Handbook of Computational Geometry. North-Holland, Amsterdam (2000)
Prömel, H.J., Steger, A.: RNC-approximation algorithms for the Steiner problem. In: Proc. Symposium on Theoretical Aspects of Computer Science, pp. 559–570 (1997)
Prömel, H.J., Steger, A., The Steiner Tree Problem: A Tour through Graphs, Algorithms and Complexity. Vieeg & Shohn (2002)
Robins, G., Zelikovsky, A.: Tighter bounds for graph Steiner tree approximation. SIAM J. Discret. Math. 19, 122–134 (2005)
Sherali, H.D., Pendyala, C.M., Rappaport, T.S.: Optimal location of transmitters for micro-cellular radio communication system design. IEEE J. Sel. Areas Commun. 14, 662–673 (1996)
Takahashi, H., Matsuyama, A.: An approximate solution for the Steiner problem in graphs. Math. Japonica 24, 573–577 (1980)
Tan, X.: Approximation algorithms for the watchman route and zookeeper’s problems. J. Discret. Appl. Math. 136, 363–376 (2004)
Tutschku, K.: Demand-based radio network planning of cellular mobile communication system. In: Infocom 98 Conference, pp. 1054–1061 (1998)
Vasquez, M., Hao, J.K.: A heuristic approach for antenna positioning in cellular networks. J. Heuristics 7, 443–472 (2001)
Zelikovsky, A.: An 11/6-approximation algorithm for the network Steiner problem. Algorithmica 9, 463–470 (1993)
Zelikovsky, A., Better approximation bounds for the network and Euclidian Steiner Tree problems. University of Virginia, 1996, CS-96-06
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ben-Shimol, Y., Ben-Moshe, B., Ben-Yehezkel, Y. et al. Automated antenna positioning algorithms for wireless fixed-access networks. J Heuristics 13, 243–263 (2007). https://doi.org/10.1007/s10732-007-9015-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10732-007-9015-5