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
npolylog(k) where n is the number of vertices and k is
the minimum treewidth of the given graphs and polylog(k) is
some polynomial in log(k). Our result generalizes Babai's
quasipolynomial-time graph isomorphism test.Comment: 52 pages, 1 figur