Abstract
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.
Joint work with Krzysztof Onak.
Time
2017-07-11 14:00 ~ 15:00Speaker
Xiaorui Sun, Google Research Fellow at Simons InstituteRoom
Room 308,School of Information Management & Engineering, Shanghai University of Finance & Economics
