## 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.

Original language | English |
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Title of host publication | SIGMETRICS'11 - Proceedings of the 2011 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems |

Publisher | Association for Computing Machinery |

Pages | 293-304 |

Number of pages | 12 |

Volume | 39 |

Edition | 1 SPEC. ISSUE |

ISBN (Print) | 9781450302623 |

DOIs | |

State | Published - 2011 |

Externally published | Yes |

Event | 2011 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2011 - San Jose, United States Duration: 7 Jun 2011 → 11 Jun 2011 |

### Conference

Conference | 2011 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2011 |
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Country/Territory | United States |

City | San Jose |

Period | 7/06/11 → 11/06/11 |

### Bibliographical note

Place of conference:USA## Keywords

- End-to-end measurements
- Hidden nodes
- Quartet tests
- Sparse random graphs
- Topology discovery