  The individualization-refinement paradigm for computing a canonical labeling
and the automorphism group of a graph is investigated. A new algorithmic design
aimed at reducing the size of the associated search space is introduced, and a
new tool, named "Traces", is presented, together with experimental results and
comparisons with existing software, such as McKay's "nauty". It is shown that
the approach presented here leads to a huge reduction in the search space,
thereby making computation feasible for several classes of graphs which are
hard for all the main canonical labeling tools in the literature.
