A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Reconstructing a Hamiltonian cycle by querying the graph: application to DNA physical mapping
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
An optimal procedure for gap closing in whole genome shotgun sequencing
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
A general approach to online network optimization problems
ACM Transactions on Algorithms (TALG)
The complete optimal stars-clustering-tree problem
Discrete Applied Mathematics
Learning a hidden graph using O( logn) queries per edge
Journal of Computer and System Sciences
Learning and Verifying Graphs Using Queries with a Focus on Edge Counting
ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
Optimally Learning Social Networks with Activations and Suppressions
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Online and stochastic survivable network design
Proceedings of the forty-first annual ACM symposium on Theory of computing
Journal of Computer and System Sciences
Completing networks using observed data
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
On the hardness and approximation of minimum topic-connected overlay
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
On the approximability of minimum topic connected overlay and its special instances
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
On the approximability and hardness of minimum topic connected overlay and its special instances
Theoretical Computer Science
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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 log2/3(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.