Abstract
In this paper we study the following problem. There are n pages which clients can request at any time. The arrival times of requests for pages are known. Several requests for the same page may arrive at different times. There is a server that needs to compute a good broadcast schedule. Outputting a page satisfies all outstanding requests for the page. The goal is to minimize the average waiting time of a client. This problem has recently been shown to be NP-hard. For any fixed α, 0 < α ≤ 1/2, we give a 1/α-speed, polynomial time algorithm with an approximation ratio of 1/1−α. For example, setting α = 1/2 gives a 2-speed, 2-approximation algorithm. In addition, we give a 4-speed, 1-approximation algorithm improving the previous bound of 6-speed, 1-approximation algorithm.
Research supported by NSF Awards CCR-9820965 and NSF CCR-0113192.
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References
S. Acharya. “Broadcast Disks”: Dissemination-based data management for asymmetric communication environments. Ph.D. Thesis, Brown University, 1998.
S. Acharya, M. Franklin, and S. Zdonik. Dissemination-based data delivery using broadcast disks. In IEEE Personal Communications, 2(6), 1995.
S. Acharya, R. Alonso, M. Franklin, and S. Zdonik. Broadcast Disks: Data management for asymmetric communications Environments. In Proc. of ACM SIGMOD International Conference on Management of Data (SIGMOD), 199–210, 1995.
D. Aksoy. On-demand data broadcast for large-scale and dynamic applications. Ph.D. Thesis, University of Maryland at College Park, 2000.
D. Aksoy, and M. Franklin. RxW: A scheduling approach for large-scale on-demand data broadcast. In IEEE/ACM Transactions On Networking, Volume 7, Number 6, 486–860, 1999.
M. H. Ammar and J. W. Wong. The design of teletext broadcast cycles. In Performance Evaluation, Vol. 5(4), 235–242, 1985.
A. Bar-Noy, R. Bhatia, J. Naor, and B. Schieber. Minimizing service and operation costs of periodic scheduling. In Proceedings of 9th Annual ACM-SIAM Symposium on Discrete Algorithms, 11–20, 1998.
Y. Bartal and S. Muthukrishnan. Minimizing maximum response time in scheduling broadcasts. In Proceedings of 11th Annual ACM-SIAM Symposium on Discrete Algorithms, 558–559, 2000.
R. Bhatia. Approximation algorithms for scheduling problems. Ph.D. Thesis, University of Maryland at College Park, 1998.
M. Charikar, S. Guha, É. Tardos, and D. Shmoys. A constant factor approximation for the k-median problem. In Proc. of 31st Annual ACM Symposium on Theory of Computing, 1–10, 1999.
C. Chekuri, S. Khanna and A. Zhu. Algorithms for minimizing weighted flow time. In Proc. of 33rd Annual ACM Symp. on Theory of Computing, 84–93, 2001.
A. L. Chervenak. Tertiary Storage: An Evaluation of New Applications. Ph.D. Thesis, UC Berkeley, 1994.
DirecPC website, http://www.direcpc.com
T. Erlebach, A. Hall. NP-Hardness of broadcast scheduling and inapproximability of single-source unsplittable min-cost flow. In Proc. of 13th Annual ACM-SIAM Symposium on Discrete Algorithms, 194–202, 2002.
Intel intercast website, http://www.intercast.com
T. S. Jayram, T. Kimbrel, R. Krauthgamer, B. Schieber, and M. Sviridenko. Online server allocation in a server farm via benefit task systems. In Proc. of 33rd Annual ACM Symp. on Theory of Computing, 540–549, 2001.
C. Kenyon, N. Schabanel, and N. Young. Polynomial-time approximation scheme for data broadcast. In Proc. of 32nd Annual ACM Symposium on Theory of Computing 659–666, 2000.
B. Kalyanasundaram, K. Pruhs, and M. Velauthapillai. Scheduling broadcasts in wireless networks. In European Symposium of Algorithms, LNCS 1879, Springer-Verlag, 290–301, 2000.
B. Kalyanasundaram and K. Pruhs. Speed is as powerful as clairvoyance. In IEEE Symposium on Foundations of Computation, 214–221, 1995.
C. Phillips, C. Stein, E. Torng, and J. Wein. Optimal time-critical scheduling via resource augmentation. In Proc. of 29th Annual ACM Symposium on Theory of Computing, 140–149, 1997.
M. S. Squillante, D. D. Yao and L. Zhang. Web traffic modelling and web server performance analysis. In Proc. of 38th IEEE Conf. on Decision and Control, 4432–4437, 1999.
H. Kaplan, R. E. Tarjan, and K. Tsioutsiouliklis. Faster kinetic heaps and their use in broadcast scheduling. In Proc. of 12th Annual ACM-SIAM Symposium on Discrete Algorithms, 836–844, 2001.
J. Wong. Broadcast Delivery. In Proc. of the IEEE, 76(12), 1988.
D. E. Knuth. The Art of Computer Programming, Volume 3. Addison-Wesley, 1973.
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Gandhi, R., Khuller, S., Kim, YA., Wan, YC.J. (2002). Algorithms for Minimizing Response Time in Broadcast Scheduling. In: Cook, W.J., Schulz, A.S. (eds) Integer Programming and Combinatorial Optimization. IPCO 2002. Lecture Notes in Computer Science, vol 2337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47867-1_30
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