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An Optimized DivideandConquer Algorithm for the ClosestPair Problem in the Planar Case
"... We present an engineered version of the divideandconquer algorithm for finding the closest pair of points, within a given set of points in the XYplane. In this version of the algorithm, only two pairwise comparisons are required in the combine step, for each point that lies in the 2δwide vertic ..."
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We present an engineered version of the divideandconquer algorithm for finding the closest pair of points, within a given set of points in the XYplane. In this version of the algorithm, only two pairwise comparisons are required in the combine step, for each point that lies in the 2δ
Cut Problems And Their Application To DivideAndConquer
, 1996
"... INTRODUCTION 5.1 One of the most important paradigms in the design and analysis of algorithms is the notion of a divideandconquer algorithm. Every undergraduate course on algorithms teaches this method as one of its staples: to solve a problem quickly, one carefully splits the problem into two s ..."
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Cited by 84 (0 self)
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INTRODUCTION 5.1 One of the most important paradigms in the design and analysis of algorithms is the notion of a divideandconquer algorithm. Every undergraduate course on algorithms teaches this method as one of its staples: to solve a problem quickly, one carefully splits the problem into two
Randomized Data Structures for the Dynamic ClosestPair Problem
, 1993
"... We describe a new randomized data structure, the sparse partition, for solving the dynamic closestpair problem. Using this data structure the closest pair of a set of n points in Ddimensional space, for any fixed D, can be found in constant time. If a frame containing all the points is known in adv ..."
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Cited by 10 (2 self)
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We describe a new randomized data structure, the sparse partition, for solving the dynamic closestpair problem. Using this data structure the closest pair of a set of n points in Ddimensional space, for any fixed D, can be found in constant time. If a frame containing all the points is known
DivideandConquer Bidirectional
"... We present a new algorithm to reduce the space complexity of heuristic search. It is most effective for problem spaces that grow polynomially with problem size, but contain large numbers of cycles. For example, the problem of finding a lowestcost cornertocorner path in a Ddimensional grid has ..."
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We present a new algorithm to reduce the space complexity of heuristic search. It is most effective for problem spaces that grow polynomially with problem size, but contain large numbers of cycles. For example, the problem of finding a lowestcost cornertocorner path in a Ddimensional grid
Practical Parallel DivideandConquer Algorithms
, 1997
"... Nested data parallelism has been shown to be an important feature of parallel languages, allowing the concise expression of algorithms that operate on irregular data structures such as graphs and sparse matrices. However, previous nested dataparallel languages have relied on a vector PRAM impleme ..."
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Cited by 7 (2 self)
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implementation layer that cannot be efficiently mapped to MPPs with high interprocessor latency. This thesis shows that by restricting the problem set to that of dataparallel divideandconquer algorithms I can maintain the expressibility of full nested dataparallel languages while achieving good
DivideandConquer for Voronoi Diagrams Revisited
, 2009
"... We show how to divide the edge graph of a Voronoi diagram into a tree that corresponds to the medial axis of an (augmented) planar domain. Division into base cases is then possible, which, in the bottomup phase, can be merged by trivial concatenation. The resulting construction algorithm—similar to ..."
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Cited by 1 (0 self)
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We show how to divide the edge graph of a Voronoi diagram into a tree that corresponds to the medial axis of an (augmented) planar domain. Division into base cases is then possible, which, in the bottomup phase, can be merged by trivial concatenation. The resulting construction algorithm
SpaceEfficient Geometric DivideandConquer Algorithms
, 2006
"... We develop a number of spaceefficient tools including an approach to simulate divideandconquer spaceefficiently, stably selecting and unselecting a subset from a sorted set, and computing the kth smallest element in one dimension from a multidimensional set that is sorted in another dimension. ..."
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Cited by 22 (5 self)
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. We then apply these tools to solve several geometric problems that have solutions using some form of divideandconquer. Specifically, we present a deterministic algorithm running in O(n log n) time using O(1) extra memory given inputs of size n for the closest pair problem and a randomized solution
Structures for the Dynamic ClosestPair Problem
"... We describe a new randomized data structure, the sparse partition, for solving the dynamic closestpair problem. Using this data structure the closest pair of a set of n points in kdimensional space, for any fixed Ic, can be found in constant time. If the points are chosen from a finite universe, a ..."
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We describe a new randomized data structure, the sparse partition, for solving the dynamic closestpair problem. Using this data structure the closest pair of a set of n points in kdimensional space, for any fixed Ic, can be found in constant time. If the points are chosen from a finite universe
DivideandConquer Approximation Algorithms via Spreading Metrics
, 1996
"... We present a novel divideandconquer paradigm for approximating NPhard graph optimization problems. The paradigm models graph optimization problems that satisfy two properties: First, a divideandconquer approach is applicable. Second, a fractional spreading metric is computable in polynomial tim ..."
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Cited by 115 (10 self)
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We present a novel divideandconquer paradigm for approximating NPhard graph optimization problems. The paradigm models graph optimization problems that satisfy two properties: First, a divideandconquer approach is applicable. Second, a fractional spreading metric is computable in polynomial
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
Results 1  10
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533,435