Packet Routing: Complexity and Algorithms

  • Britta Peis
  • Martin Skutella
  • Andreas Wiese
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5893)


Store-and-forward packet routing belongs to the most fundamental tasks in network optimization. Limited bandwidth requires that some packets cannot move to their destination directly but need to wait at intermediate nodes on their path or take detours. In particular, for time critical applications, it is desirable to find schedules that ensure fast delivery of the packets. It is thus a natural objective to minimize the makespan, i.e., the time at which the last packet arrives at its destination. In this paper we present several new ideas and techniques that lead to novel algorithms and hardness results.


Short Path Directed Graph Optimal Schedule Directed Tree Packet Switching 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Meyer auf der Heide, F., Vöcking, B.: Shortest-path routing in arbitrary networks. Journal of Algorithms 31 (1999)Google Scholar
  3. 3.
    Burkard, R.E., Dlaska, K., Klinz, B.: The quickest flow problem. ZOR — Methods and Models of Operations Research 37, 31–58 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Busch, C., Magdon-Ismail, M., Mavronicolas, M.: Universal bufferless packet switching. SIAM Journal on Computing 37, 1139–1162 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Busch, C., Magdon-Ismail, M., Mavronicolas, M., Spirakis, P.: Direct routing: Algorithms and complexity. Algorithmica 45, 45–68 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Cole, R., Ost, K., Schirra, S.: Edge-coloring bipartite multigraphs in O(E logD) time. Combinatorica 21, 5–12 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    di Ianni, M.: Efficient delay routing. Theoretical Computer Science 196, 131–151 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Erlebach, T., Jansen, K.: An optimal greedy algorithm for wavelength allocation in directed tree networks. In: Proceedings of the DIMACS Workshop on Network Design: Connectivity and Facilities Location, vol. 40, pp. 117–129. AMS (1997)Google Scholar
  9. 9.
    Erlebach, T., Jansen, K.: The complexity of path coloring and call scheduling. Theoretical Computer Science 255, 33–50 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Fleischer, L., Skutell, M.: Quickest flows over time. SIAM Journal on Computing 36, 1600–1630 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Ford, L.R., Fulkerson, D.R.: Constructing maximal dynamic flows from static flows. Operations Research 6, 419–433 (1958)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Ford, L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton (1962)zbMATHGoogle Scholar
  13. 13.
    Garey, M., Johnson, D.: Computers and Intractability: A Guide to the theory of NP-completeness. Freeman, New York (1979)zbMATHGoogle Scholar
  14. 14.
    Gargano, L., Hell, P., Perennes, S.: Colouring paths in directed symmetric trees with applications to WDM routing. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 505–515. Springer, Heidelberg (1997)Google Scholar
  15. 15.
    Hall, A., Hippler, S., Skutella, M.: Multicommodity flows over time: Efficient algorithms and complexity. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 397–409. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Hoppe, B., Tardos, E.: The quickest transshipment problem. Mathematics of Operations Research 25, 36–62 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Jansen, K.: Approximation results for wavelength routing in directed binary trees. In: Proceedings of the Workshop on Optics and Computer Science (1997)Google Scholar
  18. 18.
    Koch, R., Peis, B., Skutella, M., Wiese, A.: Real-time message routing and scheduling. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds.) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. LNCS, vol. 5687, pp. 217–230. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Leighton, F.T., Maggs, B.M., Rao, S.B.: Packet routing and job-scheduling in O(congestion + dilation) steps. Combinatorica 14, 167–186 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Leighton, F.T., Maggs, B.M., Richa, A.W.: Fast algorithms for finding O(congestion + dilation) packet routing schedules. Combinatorica 19, 375–401 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Leung, J.Y.-T.: Handbook of Scheduling: Algorithms, Models and Performance Analysis (2004)Google Scholar
  22. 22.
    Mansour, Y., Patt-Shamir, B.: Greedy packet scheduling on shortest paths. Journal of Algorithms 14 (1993)Google Scholar
  23. 23.
    Megiddo, N.: Combinatorial optimization with rational objective functions. Mathematics of Operations Research 4, 414–424 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Ostrovsky, R., Rabani, Y.: Universal O(congestion + dilation + log1 + ε N) local control packet switching algorithms. In: Proceedings of the 29th annual ACM Symposium on Theory of Computing, pp. 644–653 (1997)Google Scholar
  25. 25.
    Peis, B., Skutella, M., Wiese, A.: Packet routing: Complexity and algorithms. Technical Report 003-2009, Technische Universität Berlin (February 2009)Google Scholar
  26. 26.
    Rabani, Y., Tardos, É.: Distributed packet switching in arbitrary networks. In: Proceedings of the 28th annual ACM Symposium on Theory of Computing, pp. 366–375. ACM, New York (1996)Google Scholar
  27. 27.
    Raghavan, P., Upfal, E.: Efficient routing in all-optical networks. In: Proceedings of the 26th annual ACM Symposium on Theory of Computing, pp. 134–143. ACM, New York (1994)Google Scholar
  28. 28.
    Srinivasan, A., Teo, C.-P.: A constant-factor approximation algorithm for packet routing and balancing local vs. global criteria. SIAM Journal on Computing 30 (2001)Google Scholar
  29. 29.
    Williamson, D.P., Hall, L.A., Hoogeveen, J.A., Hurkens, C.A.J., Lenstra, J.K., Sevast’janov, S.V., Shmoys, D.B.: Short shop schedules. Operations Research 45, 288–294 (1997)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

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

Personalised recommendations