Optimal solutions for a class of point retrieval problems
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The problem of preprocessing P so that for any query point q, the points of P in C+q can be retrieved efficiently is studied, and the existence of an optimal solution is demonstrated.About:
This article is published in Journal of Symbolic Computation.The article was published on 1985-03-01 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Point (geometry).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.
Geometric Range Searching and Its Relatives
Pankaj K. Agarwal,Je Erickson +1 more
TL;DR: This volume provides an excellent opportunity to recapitulate the current status of geometric range searching and to summarize the recent progress in this area.
Journal ArticleDOI
A unified algorithm for finding maximum and minimum object enclosing rectangles and cuboids
TL;DR: In this paper, a new algorithm based on interval tree data structure is presented, which runs in O(nlogn) time and consumes O(n) space, which can be tailored for locating the position of the plate to enclose maximum or minimum number of objects with the same time and space complexity.
Proceedings ArticleDOI
Solving query-retrieval problems by compacting Voronoi diagrams
TL;DR: In this article, the authors proposed a new technique for solving a variety of query-retrieval problems in optimal time with optimal or near-optimal space, which can be used to construct algorithms and data structures for circular range searching, half-space range searching and computing k-nearest neighbors in a number of metrics.
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Linear space data structures for two types of range search
TL;DR: This paper examines thehomothetic range search problem, where a setS ofn points in the plane is to be preprocessed so that for any triangleT with sides parallel to three fixed directions the points ofS that lie inT can be computed efficiently, and looks at domination searching in three dimensions.
References
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Journal ArticleDOI
On the shape of a set of points in the plane
TL;DR: A generalization of the convex hull of a finite set of points in the plane leads to a family of straight-line graphs, "alpha -shapes," which seem to capture the intuitive notions of "fine shape" and "crude shape" of point sets.
Proceedings ArticleDOI
The power of geometric duality
TL;DR: A new formulation of the notion of duality that allows the unified treatment of a number of geometric problems is used, to solve two long-standing problems of computational geometry and to obtain a quadratic algorithm for computing the minimum-area triangle with vertices chosen among n points in the plane.
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New data structures for orthogonal range queries
TL;DR: This article introduces one new data structure which uses memory $O(N\log N)$ for supporting orthogonal range queries with worst-case complexity $O(\log ^{k - 1} N) $ and several modifications of this proposal for a dynamic environment.
Filtering searcr: a new approach to query.answering
TL;DR: This work introduces a new technique for solving problems of the following form: preprocess a set of objects so that those satisfying a given property with respect to a query object can be listed very effectively.