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Greedy Approximation Algorithms for Finding Dense Components in a Graph

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Approximation Algorithms for Combinatorial Optimization (APPROX 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1913))

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.

Research supported by the Pierre and Christine Lamond Fellowship, an ARO MURI Grant DAAH04-96-1-0007 and NSF Grant IIS-9811904. Part of this work was done while the author was visiting IBM Almaden Research Center.

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Author information

Authors and Affiliations

  1. Stanford University, Stanford, CA, 94305, USA

    Moses Charikar

Authors
  1. Moses Charikar
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Editor information

Editors and Affiliations

  1. Christian-Albrechts-Universität zu Kiel Institut für Informatik und praktische Mathematik Olshausenstr, 40, 24098, Kiel, Germany

    Klaus Jansen

  2. Computer Science Department, University of Maryland, A.V. Williams Bldg College Park, MD 20742, USA

    Samir Khuller

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© 2000 Springer-Verlag Berlin Heidelberg

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Charikar, M. (2000). Greedy Approximation Algorithms for Finding Dense Components in a Graph. In: Jansen, K., Khuller, S. (eds) Approximation Algorithms for Combinatorial Optimization. APPROX 2000. Lecture Notes in Computer Science, vol 1913. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44436-X_10

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  • DOI: https://doi.org/10.1007/3-540-44436-X_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67996-7

  • Online ISBN: 978-3-540-44436-7

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