Abstract
Unique Sink Orientations (USOs) are orientations of the hypercube graph capable of encoding many optimization problems, such as linear programming. When a USO is given in implicit form as an oracle, the USO recognition problem aims to distinguish USO from non-USO oracles. In this thesis we introduce a new type of orientation, the pseudo-USOs, which are closely related to the USO recognition problem. We derive many of their combinatorial properties, up to and including a full characterization. Using these properties, we design efficient USO recognition algorithms both in the classical and quantum models of computation.
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