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Inferring Social Networks from Outbreaks

  • Dana Angluin
  • James Aspnes
  • Lev Reyzin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6331)

Abstract

We consider the problem of inferring the most likely social network given connectivity constraints imposed by observations of outbreaks within the network. Given a set of vertices (or agents) V and constraints (or observations) S i  ⊆ V we seek to find a minimum log-likelihood cost (or maximum likelihood) set of edges (or connections) E such that each S i induces a connected subgraph of (V,E). For the offline version of the problem, we prove an Ω(log(n)) hardness of approximation result for uniform cost networks and give an algorithm that almost matches this bound, even for arbitrary costs. Then we consider the online problem, where the constraints are satisfied as they arrive. We give an O(nlog(n))-competitive algorithm for the arbitrary cost online problem, which has an Ω(n)-competitive lower bound. We look at the uniform cost case as well and give an O(n 2/3log2/3(n))-competitive algorithm against an oblivious adversary, as well as an \(\Omega(\sqrt{n})\)-competitive lower bound against an adaptive adversary. We examine cases when the underlying network graph is known to be a star or a path, and prove matching upper and lower bounds of Θ(log(n)) on the competitive ratio for them.

Keywords

Competitive Ratio Network Inference Connected Subgraph Competitive Algorithm Connectivity Query 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Dana Angluin
    • 1
  • James Aspnes
    • 1
  • Lev Reyzin
    • 2
  1. 1.Department of Computer ScienceYale UniversityNew Haven
  2. 2.Yahoo! ResearchNew York

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