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For a set P of n points in Rd, we define a new type of space decomposition. The new diagram provides an ε-approximation to the distance function associated with the Voronoi diagram of P, while being of near linear size, for d≥2. This contrasts with the standard Voronoi diagram that has Ω (n[d2]/) complexity in the worst case.
Date of Conference: 8-11 Oct. 2001