Abstract The Hausdorff Voronoi diagram of clusters of points in the plane is a generalization
of Voronoi diagrams based on the Hausdorff distance function. Its combinatorial complexity …

Abstract In the Hausdorff Voronoi diagram of a family of clusters of points in the plane, the
distance between a point t and a cluster P is measured as the maximum distance between t …

In the Hausdorff Voronoi diagram of a set of clusters of points in the plane, the distance
between a point t and a cluster P is the maximum Euclidean distance between t and a point …

Abstract In the Hausdorff Voronoi diagram of a set of point-clusters in the plane, the distance
between a point t and a cluster P is measured as the maximum distance between t and any …

We revisit the L∞ Hausdorff Voronoi diagram of clusters of points, equivalently, the L∞
Hausdorff Voronoi diagram of rectangles, and present a plane sweep algorithm for its …

We revisit the L∞ Hausdorff Voronoi diagram of clusters of points in the plane and present a
simple two-pass plane sweep algorithm to construct it. This problem is motivated by …

We show that the abstract Voronoi diagram of n sites in the plane can be constructed in time
O (n log n) by a randomized algorithm. This yields an alternative, but simpler, O (n log n) …

Given a set of points S in any dimension, we describe a deterministic algorithm for finding a
T⊂ S,| T|= O (1/ε) such that the centroid of T approximates the centroid of S within a factor 1+ …

Let d (a, b) denote the Euclidean distance between two points a, b in the plane. For a
clusterC of sites, and for a point p, define d (p, C)= max {d (p, x)∣ x∈ C} as the distance …

Given a set of sites in the plane, their order-k Voronoi diagram partitions the plane into
regions such that all points within one region have the same k nearest sites. The order-k …