Book ChapterDOI
Greedy approximation algorithms for finding dense components in a graph
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TLDR
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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Finding lasting dense subgraphs
TL;DR: This paper provides definitions for density over multiple graph snapshots, that capture different semantics of connectedness over time, and proposes a set of efficient algorithms to solve the Best Friends Forever problem.
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Graph Anomaly Detection Based on Steiner Connectivity and Density
TL;DR: This work provides a survey of the various formulations of anomaly detection in dynamic networks with a focus on “window-based” methods, and describes two classes of techniques: 1) generalizations of Steiner connectivity; and 2) dense subgraph mining.
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Randomized priority algorithms
TL;DR: This paper considers approximation ratios within the context of randomized priority algorithms, and proves inapproximation results for two well-studied optimization problems, namely facility location and makespan scheduling.
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Parallel Clique Counting and Peeling Algorithms
TL;DR: A new parallel algorithm is presented that has polylogarithmic span and is work-efficient with respect to the well-known sequential algorithm for $k$-clique listing by Chiba and Nishizeki and new parallel algorithms for producing unbiased estimations of clique counts are designed.
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Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications
TL;DR: An algorithm is devised that effectively exploits the maximality property and extracts inner-most cores directly, without first computing a complete decomposition of a multilayer network, allowing for a consistent speed up over a naïve method that simply filters out non-inner-most ones from all the cores.
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.