The Centroid of Points with Approximate Weights

Let S be a set of points in ℝd, each with a weight that is not known precisely, only known to fall within some range. What is the locus of the centroid of S? We prove that this locus is a convex polytope, the projection of a zonotope in ℝd+1. We derive complexity bounds and algorithms for the construction of these “centroid polytopes”.

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