Abstract
We address an important communication issue in wireless cellular networks that utilize Frequency Division Multiplexing (FDM) technology. In such networks, many users within the same geographical region (cell) can communicate simultaneously with other users of the network using distinct frequencies. The spectrum of the available frequencies is limited; thus, efficient solutions to the call control problem are essential. The objective of the call control problem is, given a spectrum of available frequencies and users that wish to communicate, to maximize the number of users that communicate without signal interference. We consider cellular networks of reuse distance k≥ 2 and we study the on-line version of the problem using competitive analysis.
In cellular networks of reuse distance 2, the previously best known algorithm that beats the lower bound of 3 on the competitiveness of deterministic algorithms works on networks with one frequency, achieves a competitive ratio against oblivious adversaries which is between 2.469 and 2.651, and uses a number of random bits at least proportional to the size of the network. We significantly improve this result by presenting a series of simple randomized algorithms that have competitive ratios smaller than 3, work on networks with arbitrarily many frequencies, and use only a constant number of random bits or a comparable weak random source. The best competitiveness upper bound we obtain is 7/3.
In cellular networks of reuse distance k>2, we present simple randomized on-line call control algorithms with competitive ratios which significantly beat the lower bounds on the competitiveness of deterministic ones and use only O(logk) random bits. Furthermore, we show a new lower bound on the competitiveness of on-line call control algorithms in cellular networks of reuse distance k≥ 5.
This work was partially funded by the European Union under IST FET Project ALCOM–FT, IST FET Project CRESCCO and RTN Project ARACNE.
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References
Awerbuch, B., Azar, Y., Fiat, A., Leonardi, S., Rosen, A.: Competitive On–line Competitive Algorithms for Call Admission in Optical Networks. Algorithmica 31(1), 29–43 (2001)
Awerbuch, B., Bartal, Y., Fiat, A., Rosen, A.: Competitive Non–Preemptive Call Control. In: Proccedings of the 5th Annual ACM–SIAM Symposium on Discrete Algorithms (SODA 1994), pp. 312–320 (1994)
Bartal, Y., Fiat, A., Leonardi, S.: Lower Bounds for On–line Graph Problems with Applications to On–line Circuit and Optical Routing. In: Proc. of the 28th Annual ACM Symposium on Theory of Computing, STOC 1996 (1996)
Caragiannis, I., Kaklamanis, C., Papaioannou, E.: Efficient On–Line Frequency Allocation and Call Control in Cellular Networks. Theory of Computing Systems 35, 521–543 (2002)
Erlebach, T., Jansen, K.: The Maximum Edge-Disjoint Paths Problem in Bidirected Trees. SIAM Journal on Discrete Mathematics 14(3), 326–355 (2001)
Hale, W.K.: Frequency Assignment: Theory and Applications. Proceedings of the IEEE 68(12), 1497–1514 (1980)
Janssen, J., Krizanc, D., Narayanan, L., Shende, S.: Distributed On–Line Frequency Assignment in Cellular Networks. Journal of Algorithms 36(2), 119–151 (2000)
Leonardi, S., Marchetti–Spaccamela, A., Prescuitti, A., Rosen, A.: On–line Randomized Call–Control Revisited. In: Proccedings of the 9th Annual ACM–SIAM Symposium on Discrete Algorithms (SODA 1998), pp. 323–332 (1998)
Motwani, R., Raghavan, B.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)
Pantziou, G., Pentaris, G., Spirakis, P.: Competitive Call Control in Mobile Networks. Theory of Computing Systems 35(6), 625–639 (2002)
Sleator, D., Tarjan, R.E.: Amortized Efficiency of List Update and Paging Rules. Communications of Association of Computing Machinery 28, 202–208 (1985)
Wan, P.-J., Liu, L.: Maximal Throughput in Wavelength-Routed Optical Networks. In: Multichannel Optical Networks: Theory and Practice. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 46, pp. 15–26. AMS (1998)
Yao, A.C.: Probabilistic Computations: Towards a Unified Measure of Complexity. In: Proceedings of the 17th Annual Symposium on Foundations of Computer Science (FOCS 1977), pp. 222–227 (1977)
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Caragiannis, I., Kaklamanis, C., Papaioannou, E. (2004). Simple On-Line Algorithms for Call Control in Cellular Networks. In: Solis-Oba, R., Jansen, K. (eds) Approximation and Online Algorithms. WAOA 2003. Lecture Notes in Computer Science, vol 2909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24592-6_6
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DOI: https://doi.org/10.1007/978-3-540-24592-6_6
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