Showing papers by "Mikhail J. Atallah published in 1987"
TL;DR: This work considers the problem of determining whether there exists a straight line that goes through every object in S, and gives an O(n log n γ (n) time algorithm for this problem, where γ(n) is a very slowly growing function of n.
55 citations
01 Jan 1987
TL;DR: A number of new techniques for solving many of the fundamental problems in computational geometry efficiently in parallel have linear or "almost" linear speed-ups over the best known sequential algorithms for these problems.
Abstract: In this thesis we present a number of new techniques for solving many of the fundamental problems in computational geometry efficiently in parallel. The resulting algorithms all have linear or "almost" linear speed-ups over the best known sequential algorithms for these problems. Specifically, the problems we address include the following: computing the diameter of a convex polygon, planar convex hull finding, finding a closest pair of points, polygon triangulation, 3-dimensional maxima finding, dominance counting, determining the visibility from a point, trapezoidal decomposition, and planar point location. The techniques presented are quite different from the ones used in the efficient sequential algorithms. All of our results are for the CREW PRAM or EREW PRAM computational models.
32 citations
TL;DR: It is shown that finding density-minimizing matchings is considerably harder than finding weight-minimize matchings by proving that the problem is NP-hard for general bipartite graphs.
3 citations