Constructing arrangements of lines and hyperplanes with applications

An optimal algorithm is presented for constructing an arrangement of hyperplanes in arbitrary dimensions. It relies on a combinatorial result that is of interest in its own right. The algorithm is shown to improve known worst-case time complexities for five problems: computing all order-k Voronoi diagrams, computing the λ-matrix, estimating halfspace queries, degeneracy testing, and finding the minimum volume simplex determined by a set of points.