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. 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 rules can be applied to the problem of finding the global sink of an acyclic USO. In this talk I will report some theoretical and empirical results on the worst case behaviour of various history based rules for this problem. Joint work with Yoshikazu Aoshima, Theresa Deerling, Yoshitake Matsumoto and Sonoko Moriyama
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