Topology Discovery of Sparse Random Graphs With Few Participants
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Kelner_Topology Discovery.pdf
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Author(s)
Anandkumar, Animashree
Hassidim, Avinatan
Kelner, Jonathan Adam
Date Issued
June 2011
Journal
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems, SIGMETRICS '11
Publisher
Association for Computing Machinery
Citation
Anandkumar, Animashree, Avinatan Hassidim, and Jonathan Kelner. “Topology Discovery of Sparse Random Graphs with Few Participants.” ACM Press, 2011. 293. Web.
Version
Author's final manuscript
Abstract
We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/1993744.1993774
