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Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
References
, 2013
"... Nir Ailon and Bernard Chazelle. The fast johnson–lindenstrauss transform and approximate nearest neighbors. SIAM J. Comput., 39(1):302–322, 2009. Nir Ailon, Bernard Chazelle, Seshadhri Comandur, and Ding Liu. Estimating the distance to a monotone function. Random Structures and Algorithms, 31:371–38 ..."
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Nir Ailon and Bernard Chazelle. The fast johnson–lindenstrauss transform and approximate nearest neighbors. SIAM J. Comput., 39(1):302–322, 2009. Nir Ailon, Bernard Chazelle, Seshadhri Comandur, and Ding Liu. Estimating the distance to a monotone function. Random Structures and Algorithms, 31:371–383,
Introduction by the Organisers
, 2004
"... The meeting was organized by Bernard Chazelle (Princeton), William Chen (Sydney) and Anand Srivastav (Kiel), and was attended by some twenty participants from over ten countries and three continents. The purpose of the meeting was to encourage and enhance dialogue and collaboration ..."
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The meeting was organized by Bernard Chazelle (Princeton), William Chen (Sydney) and Anand Srivastav (Kiel), and was attended by some twenty participants from over ten countries and three continents. The purpose of the meeting was to encourage and enhance dialogue and collaboration
Matching 3D Models with Shape Distributions
"... Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer vision, molecular biology, computer graphics, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, whi ..."
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Cited by 218 (7 self)
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Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer vision, molecular biology, computer graphics, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, while still discriminating between similar and dissimilar shapes. In this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is a simpler problem than the comparison of 3D surfaces by traditional shape matching methods that require pose registration, feature correspondence, or model fitting. We find that the dissimilarities be...
4. Mathematical Theory of Domains by Viggo StoltenbergHansen, Ingrid Lindstr"om, and
"... In this column we review the following books. 1. Modern Computer Algebra by Joachim von zur Gathen and J"urgen Gerhard. Reviewed by R. Gregory Taylor. This is a high level book on algorithms that do algebraic opearations on polynomials and other objects. 2. The Discrepancy MethodRandomnes ..."
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Randomness and Complexity by Bernard Chazelle. Reviewed by JinYi Cai. This is a high level book on complexity theory as it interacts with randomness. 3. Joint review of Computability and Complexity Theory by Steven Homer and Alan L. Selman, and The Complexity Theory Companion by Lane A. Hemaspaandra and Mitsunori Ogihara
appeared in Lecture Notes in Computer Science 594 (1992) 233249. On Spanning Trees with Low Crossing Numbers∗
"... Every set S of n points in the plane has a spanning tree such that no line disjoint from S has more than O( n) intersections with the tree (where the edges are embedded as straight line segments). We review the proof of this result (originally proved by Bernard Chazelle and the author in a more gene ..."
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Every set S of n points in the plane has a spanning tree such that no line disjoint from S has more than O( n) intersections with the tree (where the edges are embedded as straight line segments). We review the proof of this result (originally proved by Bernard Chazelle and the author in a more
On Spanning Trees with Low Crossing Numbers
, 1992
"... Every set S of n points in the plane has a spanning tree such that no line disjoint from S has more than O( p n) intersections with the tree (where the edges are embedded as straight line segments). We review the proof of this result (originally proved by Bernard Chazelle and the author in a more ..."
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Cited by 19 (0 self)
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Every set S of n points in the plane has a spanning tree such that no line disjoint from S has more than O( p n) intersections with the tree (where the edges are embedded as straight line segments). We review the proof of this result (originally proved by Bernard Chazelle and the author in a more
An optimal algorithm for intersecting line segments in the plane
 J. ACM
, 1992
"... Abstract. Themain contribution ofthiswork is an O(nlogr ~ +k)timeal gorithmfo rcomputingall k intersections among n line segments in the plane, This time complexity IS easdy shown to be optimal. Within thesame asymptotic cost, ouralgorithm canalso construct thesubdiwslon of theplancdefmed by the se ..."
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Cited by 182 (2 self)
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Abstract. Themain contribution ofthiswork is an O(nlogr ~ +k)timeal gorithmfo rcomputingall k intersections among n line segments in the plane, This time complexity IS easdy shown to be optimal. Within thesame asymptotic cost, ouralgorithm canalso construct thesubdiwslon of theplancdefmed by the segments and compute which segment (if any) lies right above (or below) each intersection and each endpoint. The algorithm has been implemented and performs very well. The storage requirement is on the order of n + k in the worst case, but it is considerably lower in practice. To analyze the complexity of the algorithm, an amortization argument based on a new combinatorial theorem on line arrangements is used.
A functional approach to data structures and its use in multidimensional searching
 SIAM J. Comput
, 1988
"... Abstract. We establish new upperbounds on the complexity ofmultidimensional 3earching. Our results include, in particular, linearsize data structures for range and rectangle counting in two dimensions with logarithmic query time. More generally, we give improved data structures for rectangle proble ..."
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Cited by 151 (3 self)
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Abstract. We establish new upperbounds on the complexity ofmultidimensional 3earching. Our results include, in particular, linearsize data structures for range and rectangle counting in two dimensions with logarithmic query time. More generally, we give improved data structures for rectangle problems in any dimension, in a static as well as a dynamic setting. Several ofthe algorithms we give are simple to implement and might be the solutions of choice in practice. Central to this paper is the nonstandard approach followed to achieve these results. At its rootwe find a redefinition ofdata structures interms offunctional specifications.
Approximate Nearest Neighbors and the Fast JohnsonLindenstrauss Transform
 STOC'06
, 2006
"... We introduce a new lowdistortion embedding of ℓ d 2 into O(log n) ℓp (p = 1, 2), called the FastJohnsonLindenstraussTransform. The FJLT is faster than standard random projections and just as easy to implement. It is based upon the preconditioning of a sparse projection matrix with a randomized F ..."
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Cited by 156 (6 self)
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We introduce a new lowdistortion embedding of ℓ d 2 into O(log n) ℓp (p = 1, 2), called the FastJohnsonLindenstraussTransform. The FJLT is faster than standard random projections and just as easy to implement. It is based upon the preconditioning of a sparse projection matrix with a randomized Fourier transform. Sparse random projections are unsuitable for lowdistortion embeddings. We overcome this handicap by exploiting the “Heisenberg principle” of the Fourier transform, ie, its localglobal duality. The FJLT can be used to speed up search algorithms based on lowdistortion embeddings in ℓ1 and ℓ2. We consider the case of approximate nearest neighbors in ℓ d 2. We provide a faster algorithm using classical projections, which we then further speed up by plugging in the FJLT. We also give a faster algorithm for searching over the hypercube.
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