  Research on the similarity of a graph to being a tree - called the treewidth
of the graph - has seen an enormous rise within the last decade, but a
practically fast algorithm for this task has been discovered only recently by
Tamaki (ESA 2017). It is based on dynamic programming and makes use of the fact
that the number of positive subinstances is typically substantially smaller
than the number of all subinstances. Algorithms producing only such
subinstances are called positive-instance driven (PID). We give an alternative
and intuitive view on this algorithm from the perspective of the corresponding
configuration graphs in certain two-player games. This allows us to develop
PID-algorithms for a wide range of important graph parameters such as
treewidth, pathwidth, and treedepth. We analyse the worst case behaviour of the
approach on some well-known graph classes and perform an experimental
evaluation on real world and random graphs.
