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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Journal ArticleDOI
Applications of Near-Term Photonic Quantum Computers: Software and Algorithms
Thomas R. Bromley,Juan Miguel Arrazola,Soran Jahangiri,Josh Izaac,Nicolás Quesada,Alain Delgado Gran,Maria Schuld,Jeremy Swinarton,Zeid Zabaneh,Nathan Killoran +9 more
TL;DR: A new applications layer for the Strawberry Fields photonic quantum computing library is introduced, which provides users with the necessary tools to design and implement algorithms using GBS with only a few lines of code.
Proceedings ArticleDOI
Enumerating Top-k Quasi-Cliques
TL;DR: Kernel et al. as discussed by the authors proposed a heuristic algorithm to enumerate the k largest quasi-cliques in a graph, which is based on identifying kernels of extremely dense subgraphs within a graph.
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The Performance of Deferred-Acceptance Auctions
TL;DR: What fraction of the optimal social welfare can be guaranteed by deferred-acceptance auctions in two canonical problems, knapsack auctions and combinatorial auctions with single-minded bidders, is studied.
Proceedings ArticleDOI
Extracting dense communities from telecom call graphs
TL;DR: This paper considers social networks that are derived from telephone call records, i.e, graphs in which the individual phone numbers are the nodes and the edges correspond to a telephonic contact between the two nodes they connect, and studies the problem of extracting dense communities from such telecom call graphs.
Journal ArticleDOI
Top-k overlapping densest subgraphs: approximation algorithms and computational complexity
TL;DR: The Top-k-Overlapping Densest Subgraphs problem has been shown to admit a $$\frac{1}{10}$$ 1 10 -factor approximation algorithm and the computational complexity has been left open.
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.