Extending the Tractability Border for Closest Leaf Powers

  • Michael Dom
  • Jiong Guo
  • Falk Hüffner
  • Rolf Niedermeier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3787)


The NP-complete Closest 4-Leaf Power problem asks, given an undirected graph, whether it can be modified by at most ℓ edge insertions or deletions such that it becomes a 4-leaf power. Herein, a 4-leaf power is a graph that can be constructed by considering an unrooted tree—the 4-leaf root—with leaves one-to-one labeled by the graph vertices, where we connect two graph vertices by an edge iff their corresponding leaves are at distance at most 4 in the tree. Complementing and “completing” previous work on Closest 2-Leaf Power and Closest 3-Leaf Power, we show that Closest 4-Leaf Power is fixed-parameter tractable with respect to parameter ℓ.


Maximal Clique Error Compensation Input Graph Recursive Call Output Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Michael Dom
    • 1
  • Jiong Guo
    • 1
  • Falk Hüffner
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

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