On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Information and Computation
Determining the separation of preprocessed polyhedra: a unified approach
Proceedings of the seventeenth international colloquium on Automata, languages and programming
On the zone of a surface in a hyperplane arrangement
Discrete & Computational Geometry
The nature of statistical learning theory
The nature of statistical learning theory
The Union of Convex Polyhedra in Three Dimensions
SIAM Journal on Computing
Surface Approximation and Geometric Partitions
SIAM Journal on Computing
Separating objects in the plane by wedges and strips
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
Separability by two lines and by nearly straight polygonal chains
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
Computational Geometry: Theory and Applications
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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A closed solid body separates one point set from another if it contains the former and the closure of its complement contains the latter. We present a near-linear algorithm for deciding whether two sets of n points in ℝ3 can be separated by a prism, near-quadratic algorithms for separating by a slab or a wedge, and a near-cubic algorithm for separating by a double wedge. The latter three algorithms improve the previous best known results by an order of magnitude, while the prism separability algorithm constitutes an improvement of two orders of magnitude.