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Hypercontractive inequalities via SOS, with an application to VertexCover
, 2012
"... Our main result is a formulation and proof of the reverse hypercontractive inequality in the sumofsquares (SOS) proof system. As a consequence, we show that for any constant γ> 0, the O(1/γ)round SOS/Lasserre SDP hierarchy certifies the statement “MinVertexCover(G n γ) ≥ (1 − on(1))V ”, wh ..."
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Cited by 1 (1 self)
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Our main result is a formulation and proof of the reverse hypercontractive inequality in the sumofsquares (SOS) proof system. As a consequence, we show that for any constant γ> 0, the O(1/γ)round SOS/Lasserre SDP hierarchy certifies the statement “MinVertexCover(G n γ) ≥ (1 − on(1))V
Complexity of counting subgraphs: Only the boundedness of the vertexcover number counts
"... Abstract—For a class C of graphs, #Sub(C) is the counting problem that, given a graph H from C and an arbitrary graph G, asks for the number of subgraphs of G isomorphic to H. It is known that if C has bounded vertexcover number (equivalently, the size of the maximum matching in C is bounded), the ..."
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Cited by 1 (0 self)
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Abstract—For a class C of graphs, #Sub(C) is the counting problem that, given a graph H from C and an arbitrary graph G, asks for the number of subgraphs of G isomorphic to H. It is known that if C has bounded vertexcover number (equivalently, the size of the maximum matching in C is bounded
Detecting the Solution Space of VertexCover by Mutualdeterminations and Backbones
, 2012
"... ar ..."
Parameterized Complexity
, 1998
"... the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs ..."
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Cited by 1218 (75 self)
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the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs into the toolkit of every algorithm designer. The purpose of the seminar was to bring together leading experts from all over the world, and from the diverse areas of computer science that have been attracted to this new framework. The seminar was intended as the rst larger international meeting with a specic focus on parameterized complexity, and it hopefully serves as a driving force in the development of the eld. 1 We had 49 participants from Australia, Canada, India, Israel, New Zealand, USA, and various European countries. During the workshop 25 lectures were given. Moreover, one night session was devoted to open problems and Thursday was basically used for problem discussion
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
Why a diagram is (sometimes) worth ten thousand words
 Cognitive Science
, 1987
"... We distinguish diagrammatic from sentential paperandpencil representationsof information by developing alternative models of informationprocessing systems that are informationally equivalent and that can be characterized as sentential or diagrammatic. Sentential representations are sequential, li ..."
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Cited by 777 (2 self)
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We distinguish diagrammatic from sentential paperandpencil representationsof information by developing alternative models of informationprocessing systems that are informationally equivalent and that can be characterized as sentential or diagrammatic. Sentential representations are sequential, like the propositions in a text. Dlogrammotlc representations ore indexed by location in a plane. Diogrommatic representations also typically display information that is only implicit in sententiol representations and that therefore has to be computed, sometimes at great cost, to make it explicit for use. We then contrast the computational efficiency of these representotions for solving several illustrative problems in mothematics and physics. When two representotions are informationally equivolent, their computational efficiency depends on the informationprocessing operators that act on them. Two sets of operators may differ in their copobilities for recognizing patterns, in the inferences they con carry out directly, and in their control strategies (in portitular. the control of search). Diogrommotic ond sentential representations sup
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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are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed
A survey of generalpurpose computation on graphics hardware
, 2007
"... The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware acompelling platform for computationally demanding tasks in awide variety of application domains. In this report, we describe, summarize, and analyze the l ..."
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Cited by 545 (18 self)
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The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware acompelling platform for computationally demanding tasks in awide variety of application domains. In this report, we describe, summarize, and analyze the latest research in mapping generalpurpose computation to graphics hardware. We begin with the technical motivations that underlie generalpurpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim the main body of this report at two separate audiences. First, we describe the techniques used in mapping generalpurpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second, we survey and categorize the latest developments in generalpurpose application development on graphics hardware.
A Survey of Program Slicing Techniques
 JOURNAL OF PROGRAMMING LANGUAGES
, 1995
"... A program slice consists of the parts of a program that (potentially) affect the values computed at some point of interest, referred to as a slicing criterion. The task of computing program slices is called program slicing. The original definition of a program slice was presented by Weiser in 197 ..."
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Cited by 777 (8 self)
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A program slice consists of the parts of a program that (potentially) affect the values computed at some point of interest, referred to as a slicing criterion. The task of computing program slices is called program slicing. The original definition of a program slice was presented by Weiser in 1979. Since then, various slightly different notions of program slices have been proposed, as well as a number of methods to compute them. An important distinction is that between a static and a dynamic slice. The former notion is computed without making assumptions regarding a program's input, whereas the latter relies on some specific test case. Procedures, arbitrary control flow, composite datatypes and pointers, and interprocess communication each require a specific solution. We classify static and dynamic slicing methods for each of these features, and compare their accuracy and efficiency. Moreover, the possibilities for combining solutions for different features are investigated....
A comparison and evaluation of multiview stereo reconstruction algorithms
 In IEEE CVPR
, 2006
"... This paper presents a quantitative comparison of several multiview stereo reconstruction algorithms. Until now, the lack of suitable calibrated multiview image datasets with known ground truth (3D shape models) has prevented such direct comparisons. In this paper, we rst survey multiview stereo a ..."
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Cited by 533 (15 self)
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quantitative comparison of stateoftheart multiview stereo reconstruction algorithms on six benchmark datasets. The datasets, evaluation details, and instructions for submitting new models are available online at
Results 1  10
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