Filtering search: a new approach to query answering
SIAM Journal on Computing
A randomized algorithm for closest-point queries
SIAM Journal on Computing
A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Computational Geometry: Theory and Applications
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
An optimal algorithm for intersecting three-dimensional convex polyhedra
SIAM Journal on Computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Algorithmic geometry
On range reporting, ray shooting and k-level construction
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Linear-time triangulation of a simple polygon made easier via randomization
Proceedings of the sixteenth annual symposium on Computational geometry
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Lectures on Discrete Geometry
A Method for Proving Lower Bounds for Certain Geometric Problems
A Method for Proving Lower Bounds for Certain Geometric Problems
Building Voronoi Diagrams for Convex Polygons in Linear Expected Time
Building Voronoi Diagrams for Convex Polygons in Linear Expected Time
Three problems about simple polygons
Computational Geometry: Theory and Applications
Preprocessing Imprecise Points and Splitting Triangulations
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Delaunay Triangulation of Imprecise Points Simplified and Extended
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Delaunay triangulations in O(sort(n)) time and more
Journal of the ACM (JACM)
Preprocessing Imprecise Points and Splitting Triangulations
SIAM Journal on Computing
Convex hull of imprecise points in o(n log n) time after preprocessing
Proceedings of the twenty-seventh annual symposium on Computational geometry
SIAM Journal on Computing
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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Color red and blue the n vertices of a convex polytope P in R3. Can we compute the convex hull of each color class in o(n log n)? What if we have k 2 colors? What if the colors are random? Consider an arbitrary query halfspace and call the vertices of P inside it blue: can the convex hull of the blue points be computed in time linear in their number? More generally, can we quickly compute the blue hull without looking at the whole polytope? This paper considers several instances of hereditary computation and provides new results for them. In particular, we resolve an eight-year old open problem by showing how to split a convex polytope in linear expected time.