Results 11  20
of
1,330,658
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 ..."
Abstract

Cited by 778 (5 self)
 Add to MetaCart
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
Semantic Similarity in a Taxonomy: An InformationBased Measure and its Application to Problems of Ambiguity in Natural Language
, 1999
"... This article presents a measure of semantic similarityinanisa taxonomy based on the notion of shared information content. Experimental evaluation against a benchmark set of human similarity judgments demonstrates that the measure performs better than the traditional edgecounting approach. The a ..."
Abstract

Cited by 601 (9 self)
 Add to MetaCart
This article presents a measure of semantic similarityinanisa taxonomy based on the notion of shared information content. Experimental evaluation against a benchmark set of human similarity judgments demonstrates that the measure performs better than the traditional edgecounting approach. The article presents algorithms that take advantage of taxonomic similarity in resolving syntactic and semantic ambiguity, along with experimental results demonstrating their e#ectiveness. 1. Introduction Evaluating semantic relatedness using network representations is a problem with a long history in arti#cial intelligence and psychology, dating back to the spreading activation approach of Quillian #1968# and Collins and Loftus #1975#. Semantic similarity represents a special case of semantic relatedness: for example, cars and gasoline would seem to be more closely related than, say, cars and bicycles, but the latter pair are certainly more similar. Rada et al. #Rada, Mili, Bicknell, & Blett...
The eyes have it: A task by data type taxonomy for information visualizations
 IN IEEE SYMPOSIUM ON VISUAL LANGUAGES
, 1996
"... A useful starting point for designing advanced graphical user interjaces is the Visual lnformationSeeking Mantra: overview first, zoom and filter, then details on demand. But this is only a starting point in trying to understand the rich and varied set of information visualizations that have been ..."
Abstract

Cited by 1250 (28 self)
 Add to MetaCart
A useful starting point for designing advanced graphical user interjaces is the Visual lnformationSeeking Mantra: overview first, zoom and filter, then details on demand. But this is only a starting point in trying to understand the rich and varied set of information visualizations that have been proposed in recent years. This paper offers a task by data type taxonomy with seven data types (one, two, threedimensional datu, temporal and multidimensional data, and tree and network data) and seven tasks (overview, Zoom, filter, detailsondemand, relate, history, and extracts).
Numerical integration of the Cartesian equations of motion of a system with constraints: molecular dynamics of nalkanes
 J. Comput. Phys
, 1977
"... A numerical algorithm integrating the 3N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated. The relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration. The method ..."
Abstract

Cited by 682 (6 self)
 Add to MetaCart
A numerical algorithm integrating the 3N Cartesian equations of motion of a system of N points subject to holonomic constraints is formulated. The relations of constraint remain perfectly fulfilled at each step of the trajectory despite the approximate character of numerical integration. The method
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
Abstract

Cited by 560 (10 self)
 Add to MetaCart
We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
Macroscopic strings as heavy quarks in large N gauge theory and Antide Sitter supergravity
 PHYS. J. C22
"... Maldacena has put forward large N correspondence between superconformal field theories on the brane and antide Sitter supergravity in spacetime. We study some aspects of the correspondence between N = 4 superconformal gauge theory on D3brane and maximal supergravity on adS5 × S5 by introducing mac ..."
Abstract

Cited by 510 (1 self)
 Add to MetaCart
Maldacena has put forward large N correspondence between superconformal field theories on the brane and antide Sitter supergravity in spacetime. We study some aspects of the correspondence between N = 4 superconformal gauge theory on D3brane and maximal supergravity on adS5 × S5 by introducing
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
Abstract

Cited by 886 (35 self)
 Add to MetaCart
. In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating
Parametric Shape Analysis via 3Valued Logic
, 2001
"... Shape Analysis concerns the problem of determining "shape invariants"... ..."
Abstract

Cited by 660 (79 self)
 Add to MetaCart
Shape Analysis concerns the problem of determining "shape invariants"...
An Extended Set of Fortran Basic Linear Algebra Subprograms
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1986
"... This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers. ..."
Abstract

Cited by 526 (72 self)
 Add to MetaCart
This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers.
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
Abstract

Cited by 500 (0 self)
 Add to MetaCart
divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a
Results 11  20
of
1,330,658