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)
In this paper, we define three Sperner problems on specific surfaces and prove that they are complete respectively for the classes PPAD, PPADS and PPA. This is the first time that locally 2-dimensional Sperner problems are proved to be complete for any of the polynomial parity argument classes.
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)