  An acyclic USO on a hypercube is formed by directing its edges in such as way
that the digraph is acyclic and each face of the hypercube has a unique sink
and a unique source. A path to the global sink of an acyclic USO can be modeled
as pivoting in a unit hypercube of the same dimension with an abstract
objective function, and vice versa. In such a way, Zadeh's 'least entered rule'
and other history based pivot rules can be applied to the problem of finding
the global sink of an acyclic USO. In this paper we present some theoretical
and empirical results on the existence of acyclic USOs for which the various
history based pivot rules can be made to follow a Hamiltonian path. In
particular, we develop an algorithm that can enumerate all such paths up to
dimension 6 using efficient pruning techniques. We show that Zadeh's original
rule admits Hamiltonian paths up to dimension 9 at least, and prove that most
of the other rules do not for all dimensions greater than 5.
