Open AccessBook
Algorithms in Combinatorial Geometry
TLDR
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.Abstract:
This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems. Combinatorial investigations play an important role in this study.read more
Citations
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MonographDOI
Planning Algorithms: Introductory Material
TL;DR: This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms, into planning under differential constraints that arise when automating the motions of virtually any mechanical system.
Proceedings ArticleDOI
Approximate nearest neighbors: towards removing the curse of dimensionality
Piotr Indyk,Rajeev Motwani +1 more
TL;DR: In this paper, the authors present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces, for data sets of size n living in R d, which require space that is only polynomial in n and d.
Journal ArticleDOI
Voronoi diagrams—a survey of a fundamental geometric data structure
TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
Proceedings Article
Similarity Search in High Dimensions via Hashing
TL;DR: Experimental results indicate that the novel scheme for approximate similarity search based on hashing scales well even for a relatively large number of dimensions, and provides experimental evidence that the method gives improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition.
Book
Introduction to Algorithms, Second Edition
TL;DR: The complexity class P is formally defined as the set of concrete decision problems that are polynomial-time solvable, and encodings are used to map abstract problems to concrete problems.
References
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Journal ArticleDOI
A note on two problems in connexion with graphs
TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
Journal ArticleDOI
Combinatorial optimization: algorithms and complexity
TL;DR: This clearly written, mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NPcomplete problems, more.
Computational geometry. an introduction
TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.
Journal ArticleDOI
Shortest connection networks and some generalizations
TL;DR: In this paper, the basic problem of interconnecting a given set of terminals with a shortest possible network of direct links is considered, and a set of simple and practical procedures are given for solving this problem both graphically and computationally.