Abstract
Admission control (call control) is a well-studied online problem. We are given a fixed graph with edge capacities, and must process a sequence of calls that arrive over time, accepting some and rejecting others in order to stay within capacity limitations of the network. In the standard theoretical formulation, this problem is analyzed as a benefit problem: the goal is to devise an online algorithm that accepts at least a reasonable fraction of the maximum number of calls that could possibly have been accepted in hindsight. This formulation, however, has the property that even algorithms with optimal competitive ratios (typically O(logn)) may end up rejecting the vast majority of calls even when it would have been possible in hindsight to reject only very few.
In this paper, we instead consider the goal of approximately minimizing the number of calls rejected. This is much more natural for real-world settings in which rejections are intended to be rare events. In order to avoid trivial lower-bounds, we assume preemption is allowed and that calls are given to the algorithm as fixed paths. We show that in a number of cases, we can in fact achieve a competitive ratio of 2 for rejections (so if the optimal in hindsight rejects 0 then we reject 0; if the optimal rejects r then we reject at most 2r). For other cases we get worse but nontrivial bounds. For the most general case of fixed paths in arbitrary graphs with arbitrary edge capacities, we achieve matching Θ(√m) upper and lower bounds. We also show a connection between these problems and online versions of the vertex-cover and set-cover problems (our factor-2 results give 2-approximations to slight generalizations of the vertex cover problem, much as [AAA99] show hardness results for the benefit version based on the hardness of approximability of independent set).
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References
R. Adler and Y. Azar. Beating the logarithmic lower bound: randomized preemptive disjoint paths and call control algorithms. In Proceedings of 10th SODA, pages 1–10, 1999.
N. Alon, U. Arad, and Y. Azar. Independent sets in hypergraphs with applications to routing via fixed paths. In Proceedings of 2nd APPROX, pages 16–27, 1999.
Baruch Awerbuch, Yossi Azar, and Serge Plotkin. Throughput-competitive online routing. In Proc. 34th Symp. Foundations of Computer Science, pages 32–40, 1993.
Baruch Awerbuch, Yair Bartal, Amos Fiat, and Adi Rosén. Competitive non-preemptive call control. In Proc. 5th Symp. on Discrete Algorithms, pages 312–320, 1994.
Baruch Awerbuch, Rainer Gawlick, Tom Leighton, and Yuval Rabani. Online admission control and circuit routing for high performance computing and communication. In Proc. 35th Symp. Foundations of Computer Science, pages 412–423, 1994.
Juan A. Garay and I. S. Gopal. Call preemption in communications networks. In Proc. INFOCOM’ 92, pages 1043–1050, 1992.
Juan A. Garay, I. S. Gopal, Shay Kutten, Yishay Mansour, and M. Yung. Efficient on-line call control algorithms. In Proc. 2nd Israel Symp. on Theory of Computing and Systems, pages 285–293, 1993.
A. Kamath, O. Palmon, and Serge Plotkin. Routing and admission control in general topology networks with poisson arrivals. In Proc. 7th Symp. on Discrete Algorithms, pages 269–278, 1996.
S. Leonardi. On-line network routing. In A. Fiat and G. Woeginger, editors, On-line Algorithms. Springer-Verlag, 1998.
Stefano Leonardi, Alberto Marchetti-Spaccamela, A. Presciutti, and Adi Rosèn. On-line randomized call-control revisited. In Proc. 9th Symp. on Discrete Algorithms, pages 323–332, 1998.
Serge Plotkin. Competitive routing in atm networks. IEEE J. Selected Areas in Communications, pages 1128–1136, 1995.
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Blum, A., Kalai, A., Kleinberg, J. (2001). Admission Control to Minimize Rejections. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_15
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DOI: https://doi.org/10.1007/3-540-44634-6_15
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