  The "abstract search algorithm" is a well known quantum method to find a
marked vertex in a graph. It has been applied with success to searching
algorithms for the hypercube and the two-dimensional grid. In this work we
provide an example for which that method fails to provide the best algorithm in
terms of time complexity. We analyze search algorithms in degree-3 hierarchical
networks using quantum walks driven by non-groverian coins. Our conclusions are
based on numerical simulations, but the hierarchical structures of the graphs
seems to allow analytical results.
