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Computational geometry.
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The article was published on 1978-01-01 and is currently open access. It has received 366 citations till now. The article focuses on the topics: Computational geometry.read more
Citations
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Proceedings ArticleDOI
Computing Euclidean maximum spanning trees
TL;DR: This work establishes various properties of maximum spanning trees that can be exploited to solve other geometric problems and presents an algorithm for finding a maximum-weight spanning tree of a set of set of n points in the Euclidean plane.
Journal ArticleDOI
Best and worst-case coverage problems for arbitrary paths in wireless sensor networks☆
TL;DR: This paper proposes a new coverage measure of the sensor network considering arbitrary paths that captures both the best-case and the worst-case coverage of theensor network simultaneously, enabling us to evaluate the given network in a global viewpoint.
Effective node adaption for grid-free semi-Lagrangian advection
Jörn Behrens,Armin Iske,S. Pöhn +2 more
TL;DR: Effective rules for the node adaption are proposed and the practicability of the grid-free advection method is illustrated in numerical examples by simulation of tracer transportation in the arctic stratosphere.
Approximation Algorithms for Geometric Separation Problems
TL;DR: This paper provides polynomial-time algorithms that are guaranteed to produce an answer within a logarithmic factor (O(log n), where n is the complexity of the input problem instance) of optimal.
Journal ArticleDOI
Covering point sets with two disjoint disks or squares
Sergio Cabello,J. Miguel Díaz-Báòez,Carlos Seara,J. Antoni Sellarès,Jorge Urrutia,Inmaculada Ventura +5 more
TL;DR: The analogous problem of finding two axis-aligned unit squares S"R and S"B instead of unit disks can be solved in O(nlogn) time, which is optimal, and an algorithm to solve this problem using O(n^3logn)Time is given.
References
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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.
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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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A Separator Theorem for Planar Graphs
TL;DR: In this paper, it was shown that the vertices of a planar graph can be partitioned into three sets A, B, C such that no edge joins a vertex in A with another vertex in B, neither A nor B contains more than ${2n/3}$ vertices, and C contains no more than $2.
A separator theorem for planar graphs
TL;DR: In this paper, it was shown that the vertices of a planar graph can be partitioned into three sets A,B,C such that no edge joins a vertex in A with another vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than $2.
Journal ArticleDOI
Applications of a Planar Separator Theorem
TL;DR: Any n-vertex planar graph has the property that it can be divided into components of roughly equal size by removing only O(√n) vertices, and this separator theorem in combination with a divide-and-conquer strategy leads to many new complexity results for planar graphs problems.