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HananiTutte and Monotone Drawings
"... Abstract. A drawing of a graph is xmonotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Tóth showed that if a graph has an xmonotone drawing in which every pair of edges crosses an even number of times, then the graph has ..."
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Abstract. A drawing of a graph is xmonotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Tóth showed that if a graph has an xmonotone drawing in which every pair of edges crosses an even number of times, then the graph has
HananiTutte and Related Results
, 2011
"... We are taking the view that crossings of adjacent edges are trivial, and easily got rid of. ..."
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Cited by 4 (2 self)
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We are taking the view that crossings of adjacent edges are trivial, and easily got rid of.
HananiTutte, monotone drawings, and levelplanarity
, 2011
"... A drawing of a graph is xmonotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Tóth showed that if a graph has an xmonotone drawing in which every pair of edges crosses an even number of times, then the graph has an xmonot ..."
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Cited by 2 (1 self)
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A drawing of a graph is xmonotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Tóth showed that if a graph has an xmonotone drawing in which every pair of edges crosses an even number of times, then the graph has an x
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
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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computational rule, the sumproduct algorithm operates in factor graphs to computeeither exactly or approximatelyvarious marginal functions by distributed messagepassing in the graph. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can
Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 498 (68 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
Interprocedural Slicing Using Dependence Graphs
 ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1990
"... ... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends previou ..."
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Cited by 822 (85 self)
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... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends
Greedy Function Approximation: A Gradient Boosting Machine
 Annals of Statistics
, 2000
"... Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed for additi ..."
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Cited by 951 (12 self)
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Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest{descent minimization. A general gradient{descent \boosting" paradigm is developed
A Guided Tour to Approximate String Matching
 ACM COMPUTING SURVEYS
, 1999
"... We survey the current techniques to cope with the problem of string matching allowing errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining t ..."
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Cited by 584 (38 self)
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We survey the current techniques to cope with the problem of string matching allowing errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining the problem and its relevance, its statistical behavior, its history and current developments, and the central ideas of the algorithms and their complexities. We present a number of experiments to compare the performance of the different algorithms and show which are the best choices according to each case. We conclude with some future work directions and open problems.
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