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Slowing Down Sorting Networks to Obtain Faster Sorting Algorithms
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This paper provides a general method that trims a factor of O(log n) time for many applications of this technique.Abstract:
Megiddo introduced a technique for using a parallel algorithm for one problem to construct an efficient serial algorithm for a second problem. We give a general method that trims a factor o f 0(logn) time (or more) for many applications of this technique.read more
Citations
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Journal ArticleDOI
Computing the fréchet distance between two polygonal curves
Helmut Alt,Michael Godau +1 more
TL;DR: As a measure for the resemblance of curves in arbitrary dimensions the authors consider the so-called Frechet-distance, which is compatible with parametrizations of the curves, and for polygonal chains P and Q consisting of p and q edges an algorithm of runtime O(pq log( pq))) measuring the Frechet Distance.
Journal ArticleDOI
Efficient algorithms for geometric optimization
Pankaj K. Agarwal,Micha Sharir +1 more
TL;DR: A wide range of applications of parametric searching and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other query-type problems.
Journal ArticleDOI
Computational Geometry—A Survey
TL;DR: The state of the art of computational geometry is surveyed, a discipline that deals with the complexity of geometric problems within the framework of the analysis of algorithms.
Book ChapterDOI
Discrete Geometric Shapes: Matching, Interpolation, and Approximation
Helmut Alt,Leonidas J. Guibas +1 more
TL;DR: This chapter surveys geometric techniques which have been used to measure the similarity or distance between shapes, as well as to approximate shapes, or interpolate between shapes.
Journal ArticleDOI
Applications of parametric searching in geometric optimization
TL;DR: The goal is to demonstrate the versatility of the parametric searching technique and obtain efficient solutions to several problems of Megiddo's parametric search technique.
References
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Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Journal ArticleDOI
Linear-Time Algorithms for Linear Programming in $R^3 $ and Related Problems
TL;DR: A linear-time algorithm is given for the classical problem of finding the smallest circle enclosing n given points in the plane, which disproves a conjecture by Shamos and Hoey that this problem requires Ω(n log n) time.
Journal ArticleDOI
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
TL;DR: It is pointed out that analyses of parallelism in computational problems have practical implications even when multi-processor machines are not available, and a unified framework for cases like this is presented.
Proceedings ArticleDOI
An 0(n log n) sorting network
TL;DR: A sorting network of size 0(n log n) and depth 0(log n) is described, and a derived procedure (&egr;-nearsort) are described below, and the sorting network will be centered around these elementary steps.
Proceedings ArticleDOI
Linear-time algorithms for linear programming in R3 and related problems
TL;DR: A linear-time algorithm is given for the classical problem of finding the smallest circle enclosing n given points in the plane, which disproves a conjecture by Shamos and Hoey that this problem requires Ω(n log n) time.