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51,023
Certifying algorithms for recognizing interval graphs and permutation graphs
- SIAM J. COMPUT
, 2006
"... A certifying algorithm for a problem is an algorithm that provides a certificate with each answer that it produces. The certificate is a piece of evidence that proves that the answer has not been compromised by a bug in the implementation. We give linear-time certifying algorithms for recognition o ..."
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Cited by 44 (8 self)
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of interval graphs and permutation graphs, and for a few other related problems. Previous algorithms fail to provide supporting evidence when they claim that the input graph is not a member of the class. We show that our certificates of nonmembership can be authenticated in O(|V|) time.
Certifying Algorithms for Recognizing Interval Graphs andPermutation Graphs
"... O(jVj) time. 1 Introduction A recognition algorithm is an algorithm that decideswhether some given input (graph, geometrical object, picture, etc.) has a certain property. Such an al-gorithm accepts the input if it has the property, and rejects it if it does not. A certifying algorithm for adecision ..."
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for adecision problem is an algorithm that also provides a certificate with each acceptance or rejection. Thecertificate proves the correctness of the answer. We give linear-time certifying algorithms forrecognition of interval graphs and permutation graphs. Previous algorithms fail to provide support-ing
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
A Graduated Assignment Algorithm for Graph Matching
, 1996
"... A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated non-convexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational comp ..."
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Cited by 378 (16 self)
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A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated non-convexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational
An Efficient Boosting Algorithm for Combining Preferences
, 1999
"... The problem of combining preferences arises in several applications, such as combining the results of different search engines. This work describes an efficient algorithm for combining multiple preferences. We first give a formal framework for the problem. We then describe and analyze a new boosting ..."
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Cited by 707 (18 self)
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The problem of combining preferences arises in several applications, such as combining the results of different search engines. This work describes an efficient algorithm for combining multiple preferences. We first give a formal framework for the problem. We then describe and analyze a new
Statistical mechanics of complex networks
- Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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as random graphs, it is increasingly recognized that the topology and evolution of real
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 ffl-far 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 k-colorable or having a ae-clique (clique of density ae
Results 1 - 10
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51,023