Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Cascading divide-and-conquer: a technique for designing parallel algorithms
SIAM Journal on Computing
Visibility and intersection problems in plane geometry
Discrete & Computational Geometry
Sharp upper and lower bounds on the length of general Davenport-Schinzel Sequences
Journal of Combinatorial Theory Series A
An optimal-time algorithm for slope selection
SIAM Journal on Computing
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
Computing the longest diagonal of a simple polygon
Information Processing Letters
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
Selecting distances in the plane
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Computing the minimum Hausdorff distance for point sets under translation
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
An algorithm for generalized point location and its applications
Journal of Symbolic Computation
Approximations and optimal geometric divide-and-conquer
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Counting circular arc intersections
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Efficient hidden surface removal for objects with small union size
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Extremal polygon containment problems
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Approximate matching of polygonal shapes (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
The upper envelope of Voronoi surfaces and its applications
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
A singly exponential stratification scheme for real semi-algebraic varieties and its applications
Theoretical Computer Science
Randomized optimal algorithm for slope selection
Information Processing Letters
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Optimal algorithms for tree partitioning
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Ray Shooting and Parametric Search
Ray Shooting and Parametric Search
Computing a Segment-Center for a Planar Point Set
Computing a Segment-Center for a Planar Point Set
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Diameter, width, closest line pair, and parametric searching
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Geometric partitioning made easier, even in parallel
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
An expander-based approach to geometric optimization
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Matching shapes with a reference point
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Efficient piecewise-linear function approximation using the uniform metric: (preliminary version)
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
ACM Computing Surveys (CSUR)
A Two-Stage Framework for Polygon Retrieval
Multimedia Tools and Applications
Content based retrieval of VRML objects: an iterative and interactive approach
Proceedings of the sixth Eurographics workshop on Multimedia 2001
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We present several applications in computational geometry of Megiddo's parametric searching technique. These applications include; (1) Finding the minimum Hausdorff distance in the Euclidean metric between two polygonal regions under translation; (2) Computing the biggest line segment that can be placed inside a simple polygon; (3) Computing the smallest width annulus that can contain a given set of points in the plane; (4) Solving the 1-segment center problem—given a set of points in the plane, find a placement for a given line segment (under translation and rotation) which minimizes the largest distance from the segment to the given points; (5) Given a set of n points in 3-space, finding the largest radius r such that if we place a ball of radius r around each point, no segment connecting a pair of points is intersected by a third ball. Besides obtaining efficient solutions to all these problems (which, in every case, either improve considerably previous solutions or are the first non-trivial solutions to these problems), our goal is to demonstrate the versatility of the parametric searching technique.