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Geodesics in CAT(0) Cubical Complexes (1101.2428v1)
Published 12 Jan 2011 in math.CO, cs.CG, cs.DM, and math.MG
Abstract: We describe an algorithm to compute the geodesics in an arbitrary CAT(0) cubical complex. A key tool is a correspondence between cubical complexes of global non-positive curvature and posets with inconsistent pairs. This correspondence also gives an explicit realization of such a complex as the state complex of a reconfigurable system, and a way to embed any interval in the integer lattice cubing of its dimension.