Book ChapterDOI
Greedy approximation algorithms for finding dense components in a graph
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This paper gives simple greedy approximation algorithms for these optimization problems of finding subgraphs maximizing these notions of density for undirected and directed graphs and answers an open question about the complexity of the optimization problem for directed graphs.Abstract:
We study the problem of finding highly connected subgraphs of undirected and directed graphs. For undirected graphs, the notion of density of a subgraph we use is the average degree of the subgraph. For directed graphs, a corresponding notion of density was introduced recently by Kannan and Vinay. This is designed to quantify highly connectedness of substructures in a sparse directed graph such as the web graph. We study the optimization problems of finding subgraphs maximizing these notions of density for undirected and directed graphs. This paper gives simple greedy approximation algorithms for these optimization problems. We also answer an open question about the complexity of the optimization problem for directed graphs.read more
Citations
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Annotating the MASC Corpus with BabelNet
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Book ChapterDOI
The complexity of detecting fixed-density clusters
TL;DR: This work studies the complexity of finding a subgraph of a certain size and a certain density, where density is measured by the average degree, and asks for the possible functions γ such that γ-CLUSTER remains NP-complete or becomes solvable in polynomial time.
Journal ArticleDOI
Discovering Hierarchical Subgraphs of K-Core-Truss
TL;DR: A novel dense subgraph model is proposed, which leverages on a new type of important edges based on the basis of k-core and k-truss, and the effectiveness and efficiency of this model is shown.
Posted Content
Finding large and small dense subgraphs
TL;DR: It is shown that DalkS can be approximated efficiently, while DamkS is nearly as hard to approximate as the densest k-subgraph problem.
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On Finding Dense Common Subgraphs
TL;DR: Many of the questions left open by previous works are settled, showing NP-hardness, hardness of approximation, non-trivial approximation algorithms, and an integrality gap for a natural relaxation.
References
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Proceedings ArticleDOI
Authoritative sources in a hyperlinked environment
TL;DR: This work proposes and test an algorithmic formulation of the notion of authority, based on the relationship between a set of relevant authoritative pages and the set of \hub pages that join them together in the link structure, that has connections to the eigenvectors of certain matrices associated with the link graph.
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Trawling the Web for emerging cyber-communities
TL;DR: The subject of this paper is the systematic enumeration of over 100,000 emerging communities from a Web crawl, motivating a graph-theoretic approach to locating such communities, and describing the algorithms and algorithmic engineering necessary to find structures that subscribe to this notion.
Book ChapterDOI
The web as a graph: measurements, models, and methods
TL;DR: This paper describes two algorithms that operate on the Web graph, addressing problems from Web search and automatic community discovery, and proposes a new family of random graph models that point to a rich new sub-field of the study of random graphs, and raises questions about the analysis of graph algorithms on the Internet.
Proceedings ArticleDOI
Inferring Web communities from link topology
TL;DR: This investigation shows that although the process by which users of the Web create pages and links is very difficult to understand at a “local” level, it results in a much greater degree of orderly high-level structure than has typically been assumed.