Graph isomorphisms in quasi-polynomial time

Let us be given two graphs ${\mathrm{\Gamma }}_1$, ${\mathrm{\Gamma }}_2$ of $n$ vertices. Are they isomorphic? If they are, the set of isomorphisms from ${\mathrm{\Gamma }}_1$ to ${\mathrm{\Gamma }}_2$ can be identified with a coset $H\cdot \pi$ inside the symmetric group on $n$ elements. How do we find $\pi$ and a set of generators of $H$? The challenge of giving an always efficient algorithm answering these questions remained open for a long time. Babai has recently shown how to solve these problems – and others linked to them – in quasi-polynomial time, i.e. in time $\exp (O(\log n{)}^{O(1)})$. His strategy is based in part on the algorithm by Luks (1980/82), who solved the case of graphs of bounded degree.