Planar k-Path in Subexponential Time and Polynomial Space

  • Daniel Lokshtanov
  • Matthias Mnich
  • Saket Saurabh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6986)


In the k-Path problem we are given an n-vertex graph G together with an integer k and asked whether G contains a path of length k as a subgraph. We give the first subexponential time, polynomial space parameterized algorithm for k-Path on planar graphs, and more generally, on H-minor-free graphs. The running time of our algorithm is \(O(2^{O(\sqrt{k}\log^2 k)}n^{O(1)})\).


Planar Graph Parameterized Algorithm Polynomial Kernel Tree Decomposition Solution Path 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Daniel Lokshtanov
    • 1
  • Matthias Mnich
    • 2
  • Saket Saurabh
    • 3
  1. 1.University of CaliforniaSan DiegoUSA
  2. 2.International Computer Science InstituteBerkeleyUSA
  3. 3.The Institute of Mathematical SciencesChennaiIndia

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