Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Filtering search: a new approach to query answering
SIAM Journal on Computing
A lower bound on the complexity of the union-split-find problem
SIAM Journal on Computing
Cascading divide-and-conquer: a technique for designing parallel algorithms
SIAM Journal on Computing
Lower bounds for orthogonal range searching: I. The reporting case
Journal of the ACM (JACM)
An optimal algorithm for intersecting three-dimensional convex polyhedra
SIAM Journal on Computing
Parallel fractional cascading on hypercube multiprocessors
Computational Geometry: Theory and Applications
ACM Computing Surveys (CSUR)
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Fractional cascading revisited
Journal of Algorithms
Simplex range reporting on a pointer machine
Computational Geometry: Theory and Applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
High-speed policy-based packet forwarding using efficient multi-dimensional range matching
Proceedings of the ACM SIGCOMM '98 conference on Applications, technologies, architectures, and protocols for computer communication
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Space Decomposition Techniques for Fast Layer-4 Switching
PfHSN '99 Proceedings of the IFIP TC6 WG6.1 & WG6.4 / IEEE ComSoc TC on on Gigabit Networking Sixth International Workshop on Protocols for High Speed Networks VI
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Efficient parallel techniques for computational geometry
Efficient parallel techniques for computational geometry
Optimal and near-optimal algorithms for generalized intersection reporting on pointer machines
Information Processing Letters
Optimal and near-optimal algorithms for generalized intersection reporting on pointer machines
Information Processing Letters
Improved range searching lower bounds
Proceedings of the twenty-eighth annual symposium on Computational geometry
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Given an n-edge convex subdivision of the plane, is it possible to report its k intersections with a query line segment in O(k+$~polylog$(n)) time, using subquadratic storage? If the query is a plane and the input is a polytope with n vertices, can one achieve O(k+$~polylog$(n)) time with subcubic storage? Does any convex polytope have a boundary dominant Dobkin-Kirkpatrick hierarchy? Can fractional cascading be generalized to planar maps instead of linear lists? We prove that the answer to all of these questions is no, and we derive near-optimal solutions to these classical problems.