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352,181
Survey of Algorithms for the Convex Hull Problem
, 1999
"... This paper presents a survey of deterministic algorithms, randomized algorithms and approximation algorithms for the convex hull problem. The algorithms range from almost three decade old ones, such as Graham's and Jarvis's, to modern randomized algorithms, overviewing outputsensitive ..."
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Cited by 5 (0 self)
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This paper presents a survey of deterministic algorithms, randomized algorithms and approximation algorithms for the convex hull problem. The algorithms range from almost three decade old ones, such as Graham's and Jarvis's, to modern randomized algorithms, overviewing output
Adaptive Algorithms for Planar Convex Hull Problems?
"... Abstract. We study problems in computational geometry from the viewpoint of adaptive algorithms. Adaptive algorithms have been extensively studied for the sorting problem, and in this paper we generalize the framework to geometric problems. To this end, we think of geometric problems as permutation ..."
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Cited by 2 (0 self)
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of the presortedness. As a case study, we look into the planar convex hull problem for which we discover two natural formulations as permutation problems. An interesting phenomenon that we prove is that for one formulation the problem can be solved adaptively, but for the other formulation no adaptive
New Lower Bounds for Convex Hull Problems in Odd Dimensions
 SIAM J. Comput
, 1996
"... We show that in the worst case, Ω(n dd=2e\Gamma1 +n log n) sidedness queries are required to determine whether the convex hull of n points in R^d is simplicial, or to determine the number of convex hull facets. This lower bound matches known upper bounds in any odd dimension. Our result fo ..."
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Cited by 31 (6 self)
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We show that in the worst case, Ω(n dd=2e\Gamma1 +n log n) sidedness queries are required to determine whether the convex hull of n points in R^d is simplicial, or to determine the number of convex hull facets. This lower bound matches known upper bounds in any odd dimension. Our result
The Quickhull algorithm for convex hulls
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
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Cited by 700 (0 self)
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is implemented with floatingpoint arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick ” facets that contain all possible exact convex hulls of the input. A variation
A Framework for MultiCore Implementations of Divide and Conquer Algorithms and its Application to the Convex Hull Problem ∗
"... We present a framework for multicore implementations of divide and conquer algorithms and show its efficiency and ease of use by applying it to the fundamental geometric problem of computing the convex hull of a point set. We concentrate on the Quickhull algorithm introduced in [2]. In general the ..."
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Cited by 3 (0 self)
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We present a framework for multicore implementations of divide and conquer algorithms and show its efficiency and ease of use by applying it to the fundamental geometric problem of computing the convex hull of a point set. We concentrate on the Quickhull algorithm introduced in [2]. In general
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5248 (67 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 832 (26 self)
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We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can
Results 1  10
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352,181