  The notion of treewidth, introduced by Robertson and Seymour in their seminal
Graph Minors series, turned out to have tremendous impact on graph
algorithmics. Many hard computational problems on graphs turn out to be
efficiently solvable in graphs of bounded treewidth: graphs that can be sweeped
with separators of bounded size. These efficient algorithms usually follow the
dynamic programming paradigm.
  In the recent years, we have seen a rapid and quite unexpected development of
involved techniques for solving various computational problems in graphs of
bounded treewidth. One of the most surprising directions is the development of
algorithms for connectivity problems that have only single-exponential
dependency (i.e., $2^{O(t)}$) on the treewidth in the running time bound, as
opposed to slightly superexponential (i.e., $2^{O(t \log t)}$) stemming from
more naive approaches. In this work, we perform a thorough experimental
evaluation of these approaches in the context of one of the most classic
connectivity problem, namely Hamiltonian Cycle.
