NP-Hardness of Broadcast Scheduling and Inapproximability of Single-Source Unsplittable Min-Cost Flow
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We consider the version of broadcast scheduling where a server can transmit W messages of a given set at each time-step, answering previously made requests for these messages. The goal is to minimize the average response time (ART) if the amount of requests is known in advance for each time-step and message. We prove that this problem is NP-hard, thus answering an open question stated by Kalyanasundaram, Pruhs and Velauthapillai (Proceedings of ESA 2000, LNCS 1879, 2000, pp. 290–301). Furthermore, we present an approximation algorithm that is allowed to send several messages at once. Using six channels for transmissions, the algorithm achieves an ART that is at least as good as the optimal solution using one channel.
From the NP-hardness of broadcast scheduling we derive a new inapproximability result of (2 − ε, 1) for the (congestion, cost) bicriteria version of the single source unsplittable min-cost flow problem, for arbitrary ε > 0. The result holds even in the often considered case where the maximum demand is less than or equal to the minimum edge capacity (d max ≤ u min), a case for which an algorithm with ratio (3, 1) was presented by Skutella.
- Acharya, S. and S. Muthukrishnan, “Scheduling on-demand broadcasts: new metrics and algorithms,” in Proceedings of the 4th Annual ACM/IEEE International Conference on Mobile Computing and Networking (Mobicom), 1998, pp. 43–54.
- Bar-Noy, A., R. Bhatia, J. Naor, and B. Schieber, “Minimizing service and operation costs of periodic scheduling,” in Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 1998, pp. 11–20.
- Bartal, Y. and S. Muthukrishnan, “Minimizing maximum response time in scheduling broadcasts,” in Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2000, pp. 558–559.
- Dinitz, Y., N. Garg, and M. Goemans, “On the single source unsplittable flow problem,” Combinatorica, 19, pp. 1–25, (1999). CrossRef
- Edmonds, J. and K. Pruhs, “Broadcast Scheduling: When Fairness is Fine,” in Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2002, pp. 421–430.
- Gandhi, R., S. Khuller, Y.-A. Kim, and Y.-C. Wan, “Algorithms for minimizing response time in broadcast scheduling,” in Proceedings of the 9th Conference on Integer Programming and Combinatorial Optimization (IPCO), 2002, pp. 425–438, Springer LNCS 2337.
- Kalyanasundaram, B. and K. Pruhs, “Speed is as powerful as clairvoyance,” J. ACM, 47, 617–643 (2000). CrossRef
- Kalyanasundaram, B., K. Pruhs, and M. Velauthapillai, “Scheduling broadcasts in wireless networks,” in Proceedings of the 8th Annual European Symposium on Algorithms (ESA), 2000, pp. 290–301, Springer LNCS 1879.
- Kenyon, C. and N. Schabanel, “The data broadcast problem with non-uniform transmission times,” in Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 1999, pp. 547–556.
- Kenyon, C., N. Schabanel, and N. Young, “Polynomial-Time approximation scheme for data broad cast,” in Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (STOC), 2000, pp. 659–666.
- Phillips, C., C. Stein, E. Torng, and J. Wein, “Optimal time-critical scheduling via resource augmentation,” in Proceedings of the 29th Annual ACM Symposium on Theory of Computing (STOC), 1997, pp. 140–149.
- Pruhs, K. and P. Uthaisombut, “A comparison of multicast pull models,” in Proceedings of the 10th Annual European Symposium on Algorithms (ESA), 2002, pp. 808–819, Springer LNCS 2461.
- N. Schabanel, “The data broadcast problem with preemption,” in Proceedings of the 17th International Symposium on Theoretical Aspects of Computer Science (STACS), 2000, pp. 181–192, Springer LNCS 1770.
- M. Skutella, “Approximating the single source unsplittable min-cost flow problem,” Math. Program. Ser. B, 91, 493–514 (2002); Extended Abstract in the Proceedings of FOCS, 2000, pp. 136-145. CrossRef
- NP-Hardness of Broadcast Scheduling and Inapproximability of Single-Source Unsplittable Min-Cost Flow
Journal of Scheduling
Volume 7, Issue 3 , pp 223-241
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