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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Proceedings ArticleDOI
Deconstruct Densest Subgraphs
Lijun Chang,Miao Qiao +1 more
TL;DR: It is shown that the structures, the relationships and the distributions of all the densest subgraphs of a graph G can be encoded in O(L) space in an index called the ds-Index, where L denotes the maximum output size of a densmost subgraph of G.
Journal ArticleDOI
Recent Advances in Fully Dynamic Graph Algorithms – A Quick Reference Guide
TL;DR: A quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms.
Journal ArticleDOI
Mining Dense Overlapping Subgraphs in weighted protein-protein interaction networks.
TL;DR: The proposed method, called MDOS (Mining Dense Overlapping Subgraphs), can integrate the information about known complexes into a weighted protein-protein interaction network to improve the mining results.
Book ChapterDOI
On quadratic programming with a ratio objective
TL;DR: Two results are given that indicate that QP-Ratio is hard to approximate to within any constant factor: one is based on the assumption that random instances of Max k-AND areHard to approximate, and the other makes a connection to a ratio version of Unique Games.
Journal ArticleDOI
The importance of unexpectedness: Discovering buzzing stories in anomalous temporal graphs
TL;DR: A novel method is proposed that characterizes abnormal association between terms in a certain time window and leverages the graph structure induced by such anomalous associations so as to identify stories as subsets of terms that are cohesively associated in this graph.
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.
Journal ArticleDOI
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.