Events
Fall 2016

# Uncertainty Seminar

Dec 8, 2016 11:00 am – 12:30 pm

We study the edge query complexity of graph isomorphism in the property testing model for dense graphs. We give an algorithm that makes $n^{1+o(1)}$ queries, improving on the previous best bound of $O~(n^{5/4})$. Since the problem is known to require $\Omega(n)$ queries, our algorithm is optimal up to a subpolynomial factor. While trying to extend a known connection to distribution testing, discovered by Fischer and Matsliah (SICOMP 2008), one encounters a natural obstacle presented by sampling lower bounds. We circumvent these limitations by exploiting a geometric representation of the connectivity of vertices. An approximate representation of similarities between vertices can be learned with a near-linear number of queries and allows relaxed versions of sampling and distribution testing problems to be solved more efficiently.