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Anders Hansson, Gabriel Istrate. Counting preimages of TCP reordering patterns. Discrete Applied Mathematics, 156(17), pp. 3187-3193, 2008.

Abstract: Packet reordering is an important property of network traffic that
should be captured by analytical models of the Transmission Control
Protocol (TCP). We study a combinatorial problem motivated by RESTORED, a TCP modeling methodology that
incorporates information about packet dynamics. A significant
component of this model is a many-to-one mapping $B$ that transforms
sequences of packet IDs into buffer sequences, in a manner that
is compatible with TCP semantics. We show that the following hold:

1. There exists a linear time algorithm that, given a buffer
sequence W of length n, decides whether there exists a permutation
A of 1,2,...,n such that $Ain B^{-1}(W)$ (and constructs
such a permutation, when it exists).

2. The problem of counting the number of permutations in $B^{-1}(W)$ has a polynomial time algorithm.

3. We also show how to extend these results to sequences of IDs
that contain repeated packets.

A preliminary version of this paper can be freely consulted at

http://www.ieat.ro:8080/IeAT/research/researchreports/igabriel.pdf/download

Keywords: TCP, packet reordering, linear algorithms, matchings

URL: http://dx.doi.org/10.1016/j.dam.2008.05.011

Posted by Gabriel Istrate

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