Maintenance of configurations in the plane
Mark H. Overmars,Jan van Leeuwen +1 more
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A fully dynamic maintenance algorithm for convex hulls that can process insertions and deletions of single points in only O(log* n) steps per transaction, where n is the number of points currently in the set.About:
This article is published in Journal of Computer and System Sciences.The article was published on 1981-10-01 and is currently open access. It has received 505 citations till now. The article focuses on the topics: Intersection (set theory) & Set (abstract data type).read more
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Algorithms in Combinatorial Geometry
TL;DR: This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems with an important role in this study.
Book
Vector models for data-parallel computing
TL;DR: A model of parallelism that extends and formalizes the Data-Parallel model on which the Connection Machine and other supercomputers are based is described, and it is argued that data-parallel models are not only practical and can be applied to a surprisingly wide variety of problems, they are also well suited for very-high-level languages and lead to a concise and clear description of algorithms and their complexity.
Journal ArticleDOI
Geometric applications of a matrix-searching algorithm
TL;DR: The Θ(m) bound on finding the maxima of wide totally monotone matrices is used to speed up several geometric algorithms by a factor of logn.
Journal ArticleDOI
Dynamic and Efficient Key Management for Access Hierarchies
TL;DR: The security of the scheme is based on pseudorandom functions, without reliance on the Random Oracle Model, and it is shown how to handle extensions proposed by Crampton [2003] of the standard hierarchies to “limited depth” and reverse inheritance.
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Geometric Approximation Algorithms
TL;DR: This book is the first to cover geometric approximation algorithms in detail, and topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings.
References
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The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
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An efficient algorith for determining the convex hull of a finite planar set
TL;DR: P can be chosen to I&E the centroid oC the triangle formed by X, y and z and Express each si E S in polar coordinates th origin P and 8 = 0 in the direction of zu~ arhitnry fixed half-line L from P.
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Time bounds for selection
TL;DR: The number of comparisons required to select the i-th smallest of n numbers is shown to be at most a linear function of n by analysis of a new selection algorithm-PICK.
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On Finding the Maxima of a Set of Vectors
TL;DR: The problem of finding all maximal elements of V with respect to the partial ordering is considered and the computational com- plexity of the problem is defined to be the number of required comparisons of two components and is denoted by Cd(n).