Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Sorting in c log n parallel steps
Combinatorica
SIAM Journal on Computing
An optimal-time algorithm for slope selection
SIAM Journal on Computing
Introduction to algorithms
Fast algorithms for collision and proximity problems involving moving geometric objects
Computational Geometry: Theory and Applications
Geometric pattern matching under Euclidean motion
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Computing the minimum diameter for moving points: an exact implementation using parametric search
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Walking your dog in the woods in polynomial time
Proceedings of the twenty-fourth annual symposium on Computational geometry
Homotopic Fréchet distance between curves or, walking your dog in the woods in polynomial time
Computational Geometry: Theory and Applications
The frechet distance revisited and extended
Proceedings of the twenty-seventh annual symposium on Computational geometry
Parametric search visualization
Proceedings of the twenty-ninth annual symposium on Computational geometry
Net and prune: a linear time algorithm for euclidean distance problems
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
The fréchet distance revisited and extended
ACM Transactions on Algorithms (TALG)
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In this paper we show that in sorting-based applications of parametric search, Quicksort can replace the parallel sorting algorithms that are usually advocated. Because of the simplicity of Quicksort, this may lead to applications of parametric search that are not only efficient in theory, but in practice as well. Also, we argue that Cole's optimization of certain parametric-search algorithms may be unnecessary under realistic assumptions about the input. Furthermore, we present a generic, flexible, and easy-to-use framework that greatly simplifies the implementation of algorithms based on parametric search. We use our framework to implement an algorithm that solves the Fréchet-distance problem. The implementation based on parametric search is faster than the binary-search approach that is often suggested as a practical replacement for the parametric-search technique.