4 research outputs found
Tight query complexity bounds for learning graph partitions
Given a partition of a graph into connected components, the membership oracle
asserts whether any two vertices of the graph lie in the same component or not.
We prove that for , learning the components of an -vertex
hidden graph with components requires at least
membership queries. Our result improves on the best known information-theoretic
bound of queries, and exactly matches the query complexity of
the algorithm introduced by [Reyzin and Srivastava, 2007] for this problem.
Additionally, we introduce an oracle, with access to which one can learn the
number of components of in asymptotically fewer queries than learning the
full partition, thus answering another question posed by the same authors.
Lastly, we introduce a more applicable version of this oracle, and prove
asymptotically tight bounds of queries for both learning
and verifying an -edge hidden graph using it.Comment: Accepted for presentation at the 35th Annual Conference of Learning
Theory, 202