Planar point location using persistent search trees
Communications of the ACM
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
Quasi-optimal range searching in spaces of finite VC-dimension
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Partitioning arrangements of lines, part I: an efficient deterministic algorithm
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Efficient binary space partitions for hidden-surface removal and solid modeling
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Hidden surface removal with respect to a moving view point
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A singly exponential stratification scheme for real semi-algebraic varieties and its applications
Theoretical Computer Science
Cutting hyperplane arrangements
Discrete & Computational Geometry
Optimal binary space partitions for orthogonal objects
Journal of Algorithms
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
On Point Location and Motion Planning Among Simplices
SIAM Journal on Computing
Algorithmic geometry
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Lectures on Discrete Geometry
The Clarkson–Shor Technique Revisited and Extended
Combinatorics, Probability and Computing
Sharp Bounds for Vertical Decompositions of Linear Arrangements in Four Dimensions
Discrete & Computational Geometry
Almost tight upper bounds for vertical decompositions in four dimensions
Journal of the ACM (JACM)
SIAM Journal on Computing
Counting and representing intersections among triangles in three dimensions
Computational Geometry: Theory and Applications
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We present new asymptotically tight bounds on cuttings, a fundamental data structure in computational geometry. For n objects in space and a parameter r ∈ N, an 1/r -cutting is a covering of the space with simplices such that the interior of each simplex intersects at most n/r objects. For n pairwise disjoint disks in R3 and a parameter r ∈ N, we construct a 1/r -cutting of size O(r2). For n axis-aligned rectangles in R3, we construct a 1/r -cutting of size O(r3/2). As an application related to multi-point location in three-space, we present tight bounds on the cost of spanning trees across barriers. Given n points and a finite set of disjoint disk barriers in R3, the points can be connected with a straight line spanning tree such that every disk cuts at most O(√n) edges of the tree. If the barriers are axis-aligned rectangles, then there is a straight line spanning tree such that every rectangle cuts O(n1/3) edges. Both bounds are the best possible.