Yves F. Verhoeven

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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)
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 Tarjan(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)
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