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Finding dense subgraphs with semidefinite programming

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Approximation Algorithms for Combinatiorial Optimization (APPROX 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1444))

Abstract

In this paper we consider the problem of computing the heaviest k-vertex induced subgraph of a given graph with nonnegative edge weights. This problem is known to be NP-hard, but its approximation complexity is not known. For the general problem only an approximation ratio of Õ(n0.3885) has been proved (Kortsarz and Peleg (1993)). In the last years several authors analyzed the case k=Ω(n). In this case Asahiro et al. (1996) showed a constant factor approximation, and for dense graphs Arora et al. (1995) obtained even a polynomial-time approximation scheme. We give a new approximation algorithm for arbitrary graphs and k=n/c for c > 1 based on semidefinite programming and randomized rounding which achieves for some c the presently best (randomized) approximation factors.

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Author information

Authors and Affiliations

  1. Mathematisches Seminar, Christian-Albrechts-UniversitÄt zu Kiel, Ludewig-Meyn-Str. 4, D-24098, Kiel, Germany

    Anand Srivastav

  2. Zentrum für Paralleles Rechnen, UniversitÄt zu Köln, Weyertal 80, D-50931, Köln, Germany

    Katja Wolf

Authors
  1. Anand Srivastav
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  2. Katja Wolf
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Klaus Jansen José Rolim

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© 1998 Springer-Verlag Berlin Heidelberg

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Srivastav, A., Wolf, K. (1998). Finding dense subgraphs with semidefinite programming. In: Jansen, K., Rolim, J. (eds) Approximation Algorithms for Combinatiorial Optimization. APPROX 1998. Lecture Notes in Computer Science, vol 1444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0053974

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  • DOI: https://doi.org/10.1007/BFb0053974

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64736-2

  • Online ISBN: 978-3-540-69067-2

  • eBook Packages: Springer Book Archive

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