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Spaceefficient planar convex hull algorithms
 Proc. Latin American Theoretical Informatics
, 2002
"... A spaceefficient algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. We describe four spaceefficient algorithms for computing the convex hull of a planar point set. ..."
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Cited by 20 (1 self)
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A spaceefficient algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. We describe four spaceefficient algorithms for computing the convex hull of a planar point set.
Optimal inplace planar convex hull algorithms
 Proceedings of Latin American Theoretical Informatics (LATIN 2002), volume 2286 of Lecture Notes in Computer Science
, 2002
"... An inplace algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. In this paper we describe three inplace algorithms for computing the convex hull of a planar point set. All three algorithms are optima ..."
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Cited by 4 (2 self)
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An inplace algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. In this paper we describe three inplace algorithms for computing the convex hull of a planar point set. All three algorithms are optimal, some more so than others...
Practical and efficient computation of additively weighted Voronoi cells for applications in molecular biology
, 1998
"... This paper is concerned with the efficient computation of additivelyweighted
Voronoi cells for applications in molecular biology. We propose a projection map for the representation of these cells leading to a surprising insight into their geometry. We present a randomized algorithm computing one suc ..."
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Cited by 1 (0 self)
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This paper is concerned with the efficient computation of additivelyweighted
Voronoi cells for applications in molecular biology. We propose a projection map for the representation of these cells leading to a surprising insight into their geometry. We present a randomized algorithm computing one such cell amidst n other spheres in expected time O(n^2 logn). Since the best known upper bound on the complexity such a cell is O(n^2), this is optimal up to a logarithmic factor. However, the experimentally observed behavior of the complexity of these cells is linear in n. In this case our algorithm performs the task in expected time O(n log^2 n). A variant of this algorithm was implemented and performs well on problem instances from molecular biology.
SpaceEfficient Planar Convex Hull Algorithms
"... A spaceefficient algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. We describe four spaceefficient algorithms for computing the convex hull of a planar point set. ..."
Abstract
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A spaceefficient algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. We describe four spaceefficient algorithms for computing the convex hull of a planar point set.
SmallDimensional Linear Programming and Convex Hulls Made Easy
"... We presenttwo randomized algorithms. One solves linear programs involving m constraints in d variables in expected time O(m). The other constructs convex hulls of n points in IR d � d> 3 � in expected time O(n bd=2c). In both bounds d is considered to be a constant. In the linear programming algo ..."
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We presenttwo randomized algorithms. One solves linear programs involving m constraints in d variables in expected time O(m). The other constructs convex hulls of n points in IR d � d> 3 � in expected time O(n bd=2c). In both bounds d is considered to be a constant. In the linear programming algorithm the dependence of the time bound on d is of the form d!. The main virtue of our results lies in the utter simplicity of the algorithms as well as their analyses. 1