SDP-Based Algorithms for Maximum Independent Set Problems on Hypergraphs

  • Geir Agnarsson
  • Magnús M. Halldórsson
  • Elena Losievskaja
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5555)


This paper deals with approximations of maximum independent sets in non-uniform hypergraphs of low degree. We obtain the first performance ratio that is sublinear in terms of the maximum or average degree of the hypergraph. We extend this to the weighted case and give a \(O(\bar{D} \log\log \bar{D}/\log \bar{D})\) bound, where \(\bar{D}\) is the average weighted degree in a hypergraph, matching the best bounds known for the special case of graphs. Our approach is to use an semi-definite technique to sparsify a given hypergraph and then apply combinatorial algorithms to find a large independent set in the resulting sparser instance.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Geir Agnarsson
    • 1
  • Magnús M. Halldórsson
    • 2
  • Elena Losievskaja
    • 3
  1. 1.Dept. of Mathematical SciencesGeorge Mason UniversityFairfaxUSA
  2. 2.School of Computer ScienceReykjavík UniversityReykjavikIceland
  3. 3.Faculty of Industrial, Mechanical Engineering and Computer ScienceUniversity of IcelandReykjavikIceland

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