Graph isomorphism problem

Can be solved in quasipolynomial \(\exp\left((\log n)^{O(1)}\right)\) time, according to this paper.

This other paper introduces a faster algorithm for graphs of small degree. This Grohe-Neuen-Schweitzer algorithm run in time \(n^{O\left((\log d)^c\right)},\) where \(n\) is the number of vertices of the input graphs, \(d\) is the maximum degree of the input graphs, and \(c\) is an absolute constant.