Topology Discovery of Sparse Random Graphs With Few Participants

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 endto-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 editdistance 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 t...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Animashree Anandkumar, Avinatan Hassidim, Jonathan A. Kelner
• Keywords: CORR 2011, Education, Participants Exchange Messages, Sparse Random Graphs, Topology Discovery