SIAM Journal on Computing
The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Computational geometry: an introduction
Computational geometry: an introduction
Constructing arrangements of lines and hyperplanes with applications
SIAM Journal on Computing
Topologically sweeping an arrangement
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
A note on lower bounds for the maximum area and maximum perimeter &kgr;-gon problems
Information Processing Letters
New methods for computing visibility graphs
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
On the zone theorem for hyperplane arrangements
SIAM Journal on Computing
A simple randomized sieve algorithm for the closest-pair problem
Information and Computation
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Discrete Applied Mathematics
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On the all-farthest-segments problem for a planar set of points
Information Processing Letters
Farthest line segment Voronoi diagrams
Information Processing Letters
An O(nlogn) algorithm for the all-farthest-segments problem for a planar set of points
Information Processing Letters
Notes on searching in multidimensional monotone arrays
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Proximity problems on line segments spanned by points
Computational Geometry: Theory and Applications
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In this paper we investigate the following type of proximity problems: given a set of n points in the plane P={p"1,p"2,p"3,...,p"n}, for each point p"i find a pair {p"j,p"k}, where ijk, such that a measure M defined on the triplet of points {p"i,p"j,p"k} is maximized or minimized. The cases where M is the distance from p"i to the segment or line defined by {p"j,p"k} have been extensively studied. We study the cases where M is the sum, product or the difference of the distances from p"i to the points p"j and p"k; distance from p"i to the line defined by p"j and p"k; the area, perimeter of the triangle defined by p"i, p"j and p"k, as well as the radius of the circumcircle defined by them. We also discuss the all-farthest triangle problem in the triangle-distance measure when P is a set of points in 3 dimensions.