Finding dense subgraphs with semidefinite programming

Extended abstract
  • Anand Srivastav
  • Katja Wolf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1444)


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.

Key words

Subgraph Problem Approximation Algorithms Randomized Algorithms Semidefinite Programming 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Anand Srivastav
    • 1
  • Katja Wolf
    • 2
  1. 1.Mathematisches SeminarChristian-Albrechts-UniversitÄt zu KielKielGermany
  2. 2.Zentrum für Paralleles RechnenUniversitÄt zu KölnKölnGermany

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