International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 1-12 | Cite as

On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism

  • Faisal N. Abu-Khzam
  • Édouard Bonnet
  • Florian SikoraEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)


Maximum Common Induced Subgraph (henceforth MCIS) is among the most studied classical \({\mathsf {NP}}\)-hard problems. MCIS remains \({\mathsf {NP}}\)-hard on many graph classes including bipartite graphs, planar graphs and k-trees. Little is known, however, about the parameterized complexity of the problem. When parameterized by the vertex cover number of the input graphs, the problem was recently shown to be fixed-parameter tractable. Capitalizing on this result, we show that the problem does not have a polynomial kernel when parameterized by vertex cover unless \({\mathsf {NP}}\subseteq \mathsf {coNP}/poly\). We also show that Maximum Common Connected Induced Subgraph (MCCIS), which is a variant where the solution must be connected, is also fixed-parameter tractable when parameterized by the vertex cover number of input graphs. Both problems are shown to be \({\mathsf {W[1]}}\)-complete on bipartite graphs and graphs of girth five and, unless \({\mathsf {P}}= {\mathsf {NP}}\), they do not belong to the class \({\mathsf {XP}}\) when parameterized by a bound on the size of the minimum feedback vertex sets of the input graphs, that is solving them in polynomial time is very unlikely when this parameter is a constant.


Induced Subgraph Isomorphism (ISI) Feedback Vertex Set Vertex Cover Number fixed-parameter Tractable Input Graph 
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.



Work partially supported by the bilateral research cooperation CEDRE between France and Lebanon (grant number 30885TM).


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Faisal N. Abu-Khzam
    • 1
  • Édouard Bonnet
    • 2
  • Florian Sikora
    • 2
    Email author
  1. 1.Lebanese American UniversityBeirutLebanon
  2. 2.PSL, Université Paris-Dauphine, LAMSADE, UMR CNRS 7243ParisFrance

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