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Combinatorics of TCP reordering

Author

Listed:
  • Anders Hansson

    (Los Alamos National Laboratory)

  • Gabriel Istrate

    (Los Alamos National Laboratory)

  • Shiva Prasad Kasiviswanathan

    (Pennsylvania State University)

Abstract

We study a combinatorial problem motivated by a receiver-oriented model of TCP traffic from Istrate et al. (2006), that incorporates information on both arrival times, and the dynamics of packet IDs. An important component of this model is a many-to-one mapping FB from sequences of IDs into a sequence of buffer sizes. We show that: i) Given a buffer sequence B, constructing a sequence A of IDs that belongs to the preimage of B is no harder than finding matchings in bipartite graph. ii) Counting the number of sequences A of packet IDs that belong to the preimage of B can be done in linear time in the special case when there exists a constant upper bound on the maximum entry in B. iii) This problem also has a fully polynomial randomized approximation scheme when we have a constant upper bound on the number of repeats in the packet sequences in the preimage. We also provide experimental evidence that the two previous results suffice to efficiently count the number of preimages for buffer sequences observed in real TCP data.

Suggested Citation

  • Anders Hansson & Gabriel Istrate & Shiva Prasad Kasiviswanathan, 2006. "Combinatorics of TCP reordering," Journal of Combinatorial Optimization, Springer, vol. 12(1), pages 57-70, September.
    • Handle: RePEc:spr:jcomop:v:12:y:2006:i:1:d:10.1007_s10878-006-8904-0
    DOI: 10.1007/s10878-006-8904-0
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