Title
Counting preimages of TCP reordering patterns
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 [G. Istrate, A. Hansson, S. Thulasidasan, M. Marathe, C. Barrett, Semantic compression of TCP traces, in: F. Boavida (Ed.), Proceedings of the Fifth IFIP NETWORKING Conference, in: Lecture Notes in Computer Science, vol. 3976, Springer-Verlag, 2006, pp. 123-135], 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 obtain the following results: *We give an easy necessary and sufficient condition for an input sequence W to be valid (i.e. A@?B^-^1(W) for some permutation A of {1,2,...,n}), and a linear time algorithm that, given a valid buffer sequence W of length n, constructs a permutation A in the preimage of W. *We show that the problem of counting the number of permutations in B^-^1(W) has a polynomial time algorithm. *We also show how to extend these results to sequences of IDs that contain repeated packets.
Year
DOI
Venue
2008
10.1016/j.dam.2008.05.011
Clinical Orthopaedics and Related Research
Keywords
DocType
Volume
doubly convex bipartite graphs,packet reordering,tcp modeling methodology,matchings.,permutation a,combinatorial problem,tcp trace,tcp semantics,tcp,input sequence w,packet dynamic,tcp reordering pattern,buffer sequence,matchings,packet ids,bipartite graph,transmission control protocol
Journal
156
Issue
ISSN
Citations 
17
Discrete Applied Mathematics
3
PageRank 
References 
Authors
0.45
7
2
Name
Order
Citations
PageRank
Anders Hansson170.95
Gabriel Istrate29924.96