Abstract
In the periodic packet routing problem a number of tasks periodically create packets which have to be transported through a network. Due to capacity constraints on the edges, it might not be possible to find a schedule which delivers all packets of all tasks in a feasible way. In this case one aims to find a feasible schedule for as many tasks as possible, or, if weights on the tasks are given, for a subset of tasks of maximal weight. In this paper we investigate this problem on trees and grids with row-column paths. We distinguish between direct schedules (i.e., schedules in which each packet is delayed only in its start vertex) and not necessarily direct schedules. For these settings we present constant factor approximation algorithms, separately for the weighted and the cardinality case.
Our results combine discrete optimization with real-time scheduling. We use new techniques which are specially designed for our problem as well as novel adaptions of existing methods.
This work was partially supported by Berlin Mathematical School and by the DFG Focus Program 1307 within the project “Algorithm Engineering for Real-time Scheduling and Routing”.
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References
Adler, M., Khanna, S., Rajaraman, R., Rosén, A.: Time-constrained scheduling of weighted packets on trees and meshes. Algorithmica 36, 123–152 (2003)
Andrews, M., Fernández, A., Harchol-Balter, M., Leighton, F., Zhang, L.: General dynamic routing with per-packet delay guarantees of O (distance + 1/session rate). SIAM Journal of Computing 30, 1594–1623 (2000)
Chekuri, C., Mydlarz, M., Shepherd, F.: Multicommodity demand flow in a tree and packing integer programs. ACM Trans. Algorithms 3, 27 (2007)
Erlebach, T., Jansen, K.: The maximum edge-disjoint paths problem in bidirected trees. SIAM Journal of Discrete Mathematics 14, 326–355 (2001)
Erlebach, T., Jansen, K.: Conversion of coloring algorithms into maximum weight independent set algorithms. Discrete Applied Mathematics 148, 107–125 (2005)
Garg, N., Vazirani, V.V., Yannakakis, M.: Primal-dual approximation algorithms for integral flow and multicut in trees. Algorithmica 18, 3–20 (1997)
Guruswami, V., Khanna, S., Rajaraman, R., Shepherd, B., Yannakakis, M.: Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems. Journal of Computer and System Sciences 67, 473–496 (2003)
Kolliopoulos, S.G., Stein, C.: Approximating disjoint-path problems using packing integer programs. Mathematical Programming 99, 63–87 (2004)
Könemann, J., Parekh, O., Pritchard, D.: Max-weight integral multicommodity flow in spiders and high-capacity trees. In: Bampis, E., Skutella, M. (eds.) WAOA 2008. LNCS, vol. 5426, pp. 1–14. Springer, Heidelberg (2009)
Peis, B., Skutella, M., Wiese, A.: Packet routing: Complexity and algorithms. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 217–228. Springer, Heidelberg (2010)
Peis, B., Stiller, S., Wiese, A.: The periodic packet routing problem. Technical Report 008-2010, Technische Universität Berlin (April 2010)
Peis, B., Wiese, A.: Throughput maximization for periodic packet scheduling. Technical Report 013-2010, Technische Universität Berlin (June 2010)
Schrijver, A.: Theory of Linear and Integer Programming. Wiley-Interscience Series in Discrete Mathematics. J. Wiley & Sons, Chichester (1986)
Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Berlin (2003)
Srinivasan, A.: Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science (FOCS), pp. 416–425 (1997)
Zuckerman, D.: Linear degree extractors and the inapproximability of max clique and chromatic number. Theory of Computing 3, 103–128 (2007)
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Peis, B., Wiese, A. (2011). Throughput Maximization for Periodic Packet Routing on Trees and Grids. In: Jansen, K., Solis-Oba, R. (eds) Approximation and Online Algorithms. WAOA 2010. Lecture Notes in Computer Science, vol 6534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18318-8_19
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DOI: https://doi.org/10.1007/978-3-642-18318-8_19
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