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Combinatorica

, Volume 19, Issue 3, pp 375–401 | Cite as

Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules

  • Tom Leighton
  • Bruce Maggs
  • Andréa W. Richa
Original Paper

O

(c+d) steps using constant-size queues, where c is the congestion of the paths in the network, and d is the length of the longest path. The proof, however, used the Lovász Local Lemma and was not constructive. In this paper, we show how to find such a schedule in \(\) time, with probability \(\), for any positive constant β, where \(\) is the sum of the lengths of the paths taken by the packets in the network, and m is the number of edges used by some packet in the network. We also show how to parallelize the algorithm so that it runs in NC. The method that we use to construct the schedules is based on the algorithmic form of the Lovász Local Lemma discovered by Beck.

AMS Subject Classification (1991) Classes:  68M20, 68M10, 68M07, 60C05 

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Copyright information

© János Bolyai Mathematical Society, 1999

Authors and Affiliations

  • Tom Leighton
    • 1
  • Bruce Maggs
    • 2
  • Andréa W. Richa
    • 3
  1. 1.Mathematics Department, and Laboratory for Computer Science, Massachusetts Institute of Technology; Cambridge, MA 02139, U.S.A.; E-mail: ftl@math.mit.eduUS
  2. 2.School of Computer Science, Carnegie Mellon University; Pittsburgh, PA 15213, U.S.A.; E-mail: bmm@cs.cmu.eduUS
  3. 3.Department of Computer Science and Engineering, Arizona State University; Tempe, AZ 85287, U.S.A.; E-mail: aricha@asu.eduUS

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