Combinatorics of TCP reordering
- 37 Downloads
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.
KeywordsBipartite Graph Buffer Size Application Layer Tree Decomposition Counting Problem
Unable to display preview. Download preview PDF.
- Bellardo J, Savage S (2002) Measuring packet reordering. In Proc. ACM SIGCOMM Internet Measurement Workshop, Marseille, France 97–105Google Scholar
- Bezákova I, Štefankovič D, Vigoda E, Vazirani VV (2006) Accelerating simulated annealing algorithm for the permanent and combinatorial counting problems. In Proceedings of the 17th ACM-SIAM Symposium on Discrete Algorithms (SODA’06), 900–907Google Scholar
- Downey RG, Fellows MR (1999) Parameterized Complexity. Springer Verlag.Google Scholar
- Istrate G, Hansson A (2005) Counting preimages of TCP reordering patterns. Submitted to Discrete Applied MathematicsGoogle Scholar
- Istrate G, Hansson A, Thulasidasan S, Marathe M, Barrett C (2006) Semantic compression of TCP traces. In Proceedings of the IFIP NETWORKING Conference, F. Boavida (editor), volume 3976 of Lecture Notes in Computer Science, Springer Verlag, 123–135Google Scholar
- Jaiswal S, Iannacone G, Diot C, Kurose J, Towsley D (2004) Inferring TCP connection characteristics through passive measurements. In Proceedings of INFOCOM’;04, volume 3, Hong Kong, China, 1582–1592Google Scholar
- Lovász L, Plummer M (1986) Matching Theory. Number 29 in Annals of Discrete Mathematics. North HollandGoogle Scholar
- Peterson L, Davie BS (2000) Computer Networks. A Systems Approach. Morgan Kauffman, San Francisco, CA, 2nd editionGoogle Scholar
- Piratla NM, Jayasumana AP, Bare AA (2005) RD: A formal, comprehensive metric for packet reordering. In Proc. IFIP Networking Conference 2005, volume 3462 of Lecture Notes in Computer Science, Springer Verlag, 78–89Google Scholar