  We extend Babai's quasipolynomial-time graph isomorphism test (STOC 2016) and
develop a quasipolynomial-time algorithm for the multiple-coset isomorphism
problem. The algorithm for the multiple-coset isomorphism problem allows to
exploit graph decompositions of the given input graphs within Babai's
group-theoretic framework.
  We use it to develop a graph isomorphism test that runs in time
$n^{\operatorname{polylog}(k)}$ where $n$ is the number of vertices and $k$ is
the minimum treewidth of the given graphs and $\operatorname{polylog}(k)$ is
some polynomial in $\operatorname{log}(k)$. Our result generalizes Babai's
quasipolynomial-time graph isomorphism test.
