# Inferring social networks from outbreaks

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.

## 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(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(n^{2/3} log^{2/3}n)-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.

- ALT 2010 proceedings version:
**PDF**.

## BibTeX

Download@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}
}

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