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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Book ChapterDOI
K-Connected Cores Computation in Large Dual Networks
TL;DR: A k-connected core (\(k\text {-}CCO\)) model in dual graphs is formulated and three algorithms for computing all maximum-connected cores (MCCO) are proposed, which are the existing \(k\ text {-]CCO\)s such that a \((k+1)\)-\(CCO%) does not exist.
Journal ArticleDOI
Density-friendly Graph Decomposition
TL;DR: A linear-time algorithm is developed that provides a factor-2 approximation to the optimal locally dense decomposition of the k-core decomposition, however, in practice k-cores have different structure than locally dense subgraphs, and as predicted by the theory, k-Cores are not always well-aligned with graph density.
Book ChapterDOI
Detecting and characterizing small dense bipartite-like subgraphs by the bipartiteness ratio measure
Angsheng Li,Pan Peng,Pan Peng +2 more
TL;DR: In this paper, the problem of finding and characterizing subgraphs with small bipartiteness ratio was studied, and a bicriteria approximation algorithm was proposed for the problem with a running time of O(e 2 θ − 2 k 1 + e ln 3 k).
Proceedings ArticleDOI
Two SDN Multi-tree Approaches for Constrained Seamless Multicast
TL;DR: This work aims to propose a Software Defined Networking SDN) architecture in which a central controller uses its knowledge of the performance and bandwidth allocation to compute redundant disjoint multicast trees.
Proceedings Article
Top-k Overlapping Densest Subgraphs: Approximation and Complexity
TL;DR: In this article, it was shown that the top-k-overlapping subgraphs problem is NP-hard even when k = 3, and that the problem is polynomial in the number of vertices in the 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.