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A number of seemingly unrelated problems involving the proximity of N points in the plane are studied, such as finding a Euclidean minimum spanning tree, the smallest circle enclosing the set, k nearest and farthest neighbors, the two closest points, and a proper straight-line triangulation. For most of the problems considered a lower bound of O(N log N) is(More)
We develop optimal algorithms for forming the intersection of geometric objects in the plane and apply them to such diverse problems as linear programming, hidden-line elimination, and wire layout. Given N line segments in the plane, finding all intersecting pairs requires O(N2) time. We give an O(N log N) algorithm to determine whether any two intersect(More)
Some of the techniques that appear to be used in biological systems have the flavor of the algorithms described here. Each of the sensory modalities makes use of some form of focus of attention. Presumably this is a mechanism to devote higher level hardware to only a portion of the data produced by lower level systems. In this way a single piece of high(More)
The complexity of a number of fundamental problems in computational geometry is examined and a number of new fast algorithms are presented and analyzed. General methods for obtaining results in geometric complexity are given and upper and lower bounds are obtained for problems involving sets of points, lines, and polygons in the plane. An effort is made to(More)
In this paper we approach the analysis of statistics algorithms from a geometric viewpoint and use techniques from computational geometry to develop new, fast algorithms for computing familiar statistical quantities. Such fundamental procedures as sorting and selection play an important role in nonparametric estimation as well as in correlation and(More)
T he recent spate of security issues and allegations of " lost votes " in the U.S. demonstrates the inadequacy of the standards used to evaluate our election systems. The current standards (the FEC Voting Systems Standards) along with the revision being developed by IEEE 1583 (see the article by Deutsch and Berger in last month's Communications) are poor(More)