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We present several results on the complexity of various forms of Sperner’s Lemma in the black-box model of computing. We give a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension. The query complexity of our algorithm is linear in the separation number of the skeleton graph of the manifold and the size of its boundary.(More)
We present several results on the complexity of various forms of Sperner's Lemma. In the black-box model of computing, we exhibit a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension. The query complexity of our algorithm is essentially linear in the separation number of the skeleton graph of the manifold and the size(More)
Let G = (V, E) be a finite graph, and f : V → N be any function. The Local Search problem consists in finding a local minimum of the function f on G, that is a vertex v such that f (v) is not larger than the value of f on the neighbors of v in G. In this note, we first prove a separation theorem slightly stronger than the one of Gilbert, Hutchinson and(More)
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