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Showing papers by "Richard Cole published in 1989"


Journal ArticleDOI
TL;DR: Improvements in parallel divide-and-conquer techniques are presented, resulting in improved parallel algorithms for a number of problems, including intersection detection, trapezoidal decomposition, and planar point location.
Abstract: Techniques for parallel divide-and-conquer are presented, resulting in improved parallel algorithms for a number of problems. The problems for which improved algorithms are given include segment intersection detection, trapezoidal decomposition, and planar point location. Efficient parallel algorithms are algo given for fractional cascading, three-dimensional maxima, two-set dominance counting, and visibility from a point. All of the algorithms presented run in $O(\log n)$ time with either a linear or a sublinear number of processors in the CREW PRAM model.

168 citations


Proceedings ArticleDOI
01 Mar 1989
TL;DR: The PRAM model provides an abstraction that strips away problems of synchronization, reliability and communication delays, thereby permitting algorithm designers to focus first and foremost on the structure of the computational problem at hand, rather than the architecture of a currently available machine.
Abstract: The PRAM model is a machine that comprises p processors and m memory cells; each processor can access each memory cell in constant time. The PRAM has proved a popular model for parallel algorithm design. For the task of designing efficient, highly parallel algorithms is quite difficult, in general. The PRAM model provides an abstraction that strips away problems of synchronization, reliability and communication delays, thereby permitting algorithm designers to focus first and foremost on the structure of the computational problem at hand, rather than the architecture of a currently available machine. As a consequence, a considerable body of PRAM algorithms has been discovered in the past several years, and a number of powerful techniques for designing such algorithms have been identified (see, for instance, the survey articles [KR88, EG88]).

161 citations


Journal ArticleDOI
TL;DR: Given n points in the plane and an integer k, the problem of selecting that pair of points that determines the line with the kth smallest or largest slope is considered and line sweeping gives an optimal, $O(n\log n)$-time algorithm.
Abstract: Given n points in the plane and an integer k, the problem of selecting that pair of points that determines the line with the kth smallest or largest slope is considered. In the restricted case, where k is $O(n)$, line sweeping gives an optimal, $O(n\log n)$-time algorithm. For general k the parametric search technique of Megiddo is used to describe an $O(n(\log n)^2 )$-time algorithm. This is modified to produce a new, optimal $O(n\log n)$-time selection algorithm by incorporating an approximation idea.

150 citations