Throughput Maximization for Periodic Packet Routing on Trees and Grids

  • Britta Peis
  • Andreas Wiese
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6534)


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.


Greedy Algorithm Throughput Maximization Feasible Schedule Start Vertex Destination Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Adler, M., Khanna, S., Rajaraman, R., Rosén, A.: Time-constrained scheduling of weighted packets on trees and meshes. Algorithmica 36, 123–152 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Chekuri, C., Mydlarz, M., Shepherd, F.: Multicommodity demand flow in a tree and packing integer programs. ACM Trans. Algorithms 3, 27 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Erlebach, T., Jansen, K.: The maximum edge-disjoint paths problem in bidirected trees. SIAM Journal of Discrete Mathematics 14, 326–355 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Erlebach, T., Jansen, K.: Conversion of coloring algorithms into maximum weight independent set algorithms. Discrete Applied Mathematics 148, 107–125 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Garg, N., Vazirani, V.V., Yannakakis, M.: Primal-dual approximation algorithms for integral flow and multicut in trees. Algorithmica 18, 3–20 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kolliopoulos, S.G., Stein, C.: Approximating disjoint-path problems using packing integer programs. Mathematical Programming 99, 63–87 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Peis, B., Stiller, S., Wiese, A.: The periodic packet routing problem. Technical Report 008-2010, Technische Universität Berlin (April 2010)Google Scholar
  12. 12.
    Peis, B., Wiese, A.: Throughput maximization for periodic packet scheduling. Technical Report 013-2010, Technische Universität Berlin (June 2010)Google Scholar
  13. 13.
    Schrijver, A.: Theory of Linear and Integer Programming. Wiley-Interscience Series in Discrete Mathematics. J. Wiley & Sons, Chichester (1986)zbMATHGoogle Scholar
  14. 14.
    Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Berlin (2003)zbMATHGoogle Scholar
  15. 15.
    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)Google Scholar
  16. 16.
    Zuckerman, D.: Linear degree extractors and the inapproximability of max clique and chromatic number. Theory of Computing 3, 103–128 (2007)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Britta Peis
    • 1
  • Andreas Wiese
    • 1
  1. 1.Technische Universität BerlinBerlinGermany

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