Dana Angluin, James Aspnes, and Lev Reyzin. Inferring social networks from outbreaks. Algorithmic Learning Theory, 21st International Conference, Lecture Notes in Computer Science 6331, Springer-Verlag, October 2010, pp. 104–118.
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) Si ⊆ V, we seek to find a minimum log-likelihood cost (or maximum likelihood) set of edges (or connections) E such that each Si 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(n log 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(n2/3 log2/3n)-competitive algorithm against an oblivious adversary, as well as an Ω(√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.
@inproceedings{AngluinAR2010outbreaks,
author = {Dana Angluin and James Aspnes and Lev Reyzin},
title = {Inferring social networks from outbreaks},
month=oct,
year = 2010,
pages = {104--118},
booktitle = {Algorithmic Learning Theory, 21st International Conference, ALT 2010, Canberra, Australia, October 6-8, 2010. Proceedings},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
volume = {6331}
}