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Facility Location and the Geometric MinimumDiameter Spanning Tree
, 2003
"... Let P be a set of n points in the plane. The geometric minimumdiameter spanning tree (MDST) of P is a tree that spans P and minimizes the Euclidian length of the longest path. It is known that there is always a mono or a dipolar MDST, i.e. a MDST with one or two nodes of degree greater 1, respecti ..."
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Cited by 5 (1 self)
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Let P be a set of n points in the plane. The geometric minimumdiameter spanning tree (MDST) of P is a tree that spans P and minimizes the Euclidian length of the longest path. It is known that there is always a mono or a dipolar MDST, i.e. a MDST with one or two nodes of degree greater 1
Approximating the Geometric MinimumDiameter Spanning Tree
 Institut für Mathematik und Informatik, Universität Greifswald
, 2002
"... Let P be a set of n points in the plane. The geometric minimumdiameter spanning tree (MDST) of P is a tree that spans P and minimizes the Euclidian length of the longest path. It is known that there is always a mono or a dipolar MDST, i.e. a MDST whose longest path consists of two or three edges, ..."
Abstract

Cited by 2 (1 self)
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Let P be a set of n points in the plane. The geometric minimumdiameter spanning tree (MDST) of P is a tree that spans P and minimizes the Euclidian length of the longest path. It is known that there is always a mono or a dipolar MDST, i.e. a MDST whose longest path consists of two or three edges
Approximating the Geometric Minimum Diameter Spanning Tree
 15 th Canadian Conference on Computational Geometry
, 2003
"... Given a set P of points in the plane, a geometric minimumdiameter spanning tree (GMDST) of P is a spanning tree of P such that the longest path through the tree is minimized. In this paper, we present an approximation algorithm that generates a tree whose diameter is no more than (1 + ɛ) times that ..."
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Cited by 1 (0 self)
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Given a set P of points in the plane, a geometric minimumdiameter spanning tree (GMDST) of P is a spanning tree of P such that the longest path through the tree is minimized. In this paper, we present an approximation algorithm that generates a tree whose diameter is no more than (1 + ɛ) times
Computing a (1 + ffl)Approximate Geometric MinimumDiameter Spanning Tree
, 2003
"... Abstract Given a set P of points in the plane, a geometric minimumdiameter spanning tree (GMDST)of P is a spanning tree of P such that the longest path through the tree is minimized. Forseveral years, the best upper bound on the time to compute a GMDST was cubic with respect to the number of points ..."
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Abstract Given a set P of points in the plane, a geometric minimumdiameter spanning tree (GMDST)of P is a spanning tree of P such that the longest path through the tree is minimized. Forseveral years, the best upper bound on the time to compute a GMDST was cubic with respect to the number
Computing a (1+ɛ)approximate geometric minimumdiameter spanning tree. Private communication
, 2002
"... Given a set P of points in the plane, a geometric minimumdiameter spanning tree (GMDST) of P is a spanning tree of P such that the longest path through the tree is minimized. For several years, the best upper bound on the time to compute a GMDST was cubic with respect to the number of points in the ..."
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Cited by 1 (0 self)
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Given a set P of points in the plane, a geometric minimumdiameter spanning tree (GMDST) of P is a spanning tree of P such that the longest path through the tree is minimized. For several years, the best upper bound on the time to compute a GMDST was cubic with respect to the number of points
Geometric Minimum Diameter Minimum Cost Spanning Tree Problem
"... Abstract. In this paper we consider bicriteria geometric optimization problems, in particular, the minimum diameter minimum cost spanning tree problem and the minimum radius minimum cost spanning tree problem for a set of points in the plane. The former problem is to construct a minimum diameter s ..."
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Abstract. In this paper we consider bicriteria geometric optimization problems, in particular, the minimum diameter minimum cost spanning tree problem and the minimum radius minimum cost spanning tree problem for a set of points in the plane. The former problem is to construct a minimum diameter
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings
Multiresolution Analysis of Arbitrary Meshes
, 1995
"... In computer graphics and geometric modeling, shapes are often represented by triangular meshes. With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace. Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit. Multire ..."
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Cited by 605 (16 self)
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In computer graphics and geometric modeling, shapes are often represented by triangular meshes. With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace. Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit
A Tutorial on Visual Servo Control
 IEEE Transactions on Robotics and Automation
, 1996
"... This paper provides a tutorial introduction to visual servo control of robotic manipulators. Since the topic spans many disciplines our goal is limited to providing a basic conceptual framework. We begin by reviewing the prerequisite topics from robotics and computer vision, including a brief review ..."
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Cited by 822 (25 self)
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review of coordinate transformations, velocity representation, and a description of the geometric aspects of the image formation process. We then present a taxonomy of visual servo control systems. The two major classes of systems, positionbased and imagebased systems, are then discussed. Since any
Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations
, 2005
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
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Cited by 534 (48 self)
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How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include heavy tails for in and outdegree distributions, communities, smallworld phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time. Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing superlinearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) orO(log(log n)). Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a “forest fire” spreading process, that has a simple, intuitive justification, requires very few parameters (like the “flammability” of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study.
Results 1  10
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107,789