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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$(1-\epsilon)$-approximate fully dynamic densest subgraph: linear space and faster update time
Chandra Chekuri,Kent Quanrud +1 more
TL;DR: A data structure for (1 − ǫ )-approximate DSG that improves the one from [ SW20] in two aspects and extends in a natural fashion to hypergraphs and yields improvements in space and update times over recent work [BBCG22] that builds upon [SW20].
Dissertation
Bridging methodological gaps in network-based systems biology
TL;DR: This work proposes a novel network-based approach to functional enrichment that explicitly accounts for these underlying molecular interactions and demonstrates the efficacy of Linker through two applications: proposing extensions to an existing model of cell cycle regulation in budding yeast and automated reconstruction of human signaling pathways.
Proceedings ArticleDOI
Anchored Densest Subgraph
Yizhou Dai,Miao Qiao,Lijun Chang +2 more
TL;DR: This paper proposes an algorithm that is local since the complexity is only related to the nodes in S as opposed to the entire graph, which outperforms existing local community detection solutions in locality, result density, and query processing time and space.
Book ChapterDOI
Biological Pathway Analysis
TL;DR: This article focuses on network-based approaches to analyze biological pathways, and introduces some of the algorithms that have been proposed to compare and align biological pathways and briefly discusses applications in the context of GWAS.
Posted Content
The Generalized Mean Densest Subgraph Problem
TL;DR: In this paper, the authors introduce a new family of dense subgraph objectives, parameterized by a single parameter $p, based on computing generalized means of degree sequences of a subgraph.
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.