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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
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
The DivideandConquer Manifesto
 Proceedings of the Eleventh International Conference on Algorithmic Learning Theory
, 2000
"... . Existing machine learning theory and algorithms have focused on learning an unknown function from training examples, where the unknown function maps from a feature vector to one of a small number of classes. Emerging applications in science and industry require learning much more complex funct ..."
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Cited by 4 (0 self)
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applications. These systems all employ some form of divideandconquer, where the inputs and outputs are divided into smaller pieces (e.g., "windows"), classified, and then the results are merged to produce an overall solution. This paper defines the problem of divideandconquer learning
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
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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hard. We prove that (1 \Gamma o(1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low order terms) between the ratio of approximation achievable by the greedy algorithm (which is (1 \Gamma
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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to be discarded again. The algorithm works for polygonal and curved objects as sites and, in particular, for circular arcs which allows its extension to general freeform objects by Voronoi diagram preserving and data saving biarc approximations. The algorithm is randomized, with expected runtime O(nlog n) under
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
A DivideandConquer Algorithm for
"... Abstract. The problem of efficiently computing the betweenness centrality of nodes has been researched extensively. To date, the best known exact and centralized algorithm for this task is an algorithm proposed in 2001 by Brandes [7]. The contribution of our paper is Brandes++, an algorithm for ex ..."
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Abstract. The problem of efficiently computing the betweenness centrality of nodes has been researched extensively. To date, the best known exact and centralized algorithm for this task is an algorithm proposed in 2001 by Brandes [7]. The contribution of our paper is Brandes++, an algorithm
A DivideandConquer Approach to Quad Remeshing
"... Abstract—Many natural and manmade objects consist of simple primitives, similar components, and various symmetry structures. This paper presents a divideandconquer quadrangulation approach that exploits such global structural information. Given a model represented in triangular mesh, we first seg ..."
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Abstract—Many natural and manmade objects consist of simple primitives, similar components, and various symmetry structures. This paper presents a divideandconquer quadrangulation approach that exploits such global structural information. Given a model represented in triangular mesh, we first
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