Finding Dense Subgraphs of Sparse Graphs

  • Christian Komusiewicz
  • Manuel Sorge
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7535)


We investigate the computational complexity of the Densest- k -Subgraph (D k S) problem, where the input is an undirected graph G = (V,E) and one wants to find a subgraph on exactly k vertices with a maximum number of edges. We extend previous work on D k S by studying its parameterized complexity. On the positive side, we show that, when fixing some constant minimum density μ of the sought subgraph, D k S becomes fixed-parameter tractable with respect to either of the parameters maximum degree and h-index of G. Furthermore, we obtain a fixed-parameter algorithm for D k S with respect to the combined parameter “degeneracy of G and |V| − k”. On the negative side, we find that D k S is W[1]-hard with respect to the combined parameter “solution size k and degeneracy of G”. We furthermore strengthen a previous hardness result for D k S [Cai, Comput. J., 2008] by showing that for every fixed μ, 0 < μ < 1, the problem of deciding whether G contains a subgraph of density at least μ is W[1]-hard with respect to the parameter |V| − k.


Maximum Degree Input Graph Sparse Graph Enumeration Algorithm Combine Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christian Komusiewicz
    • 1
  • Manuel Sorge
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany

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