Closest 4-leaf power is fixed-parameter tractable

  • Authors:

  • Michael Dom;Jiong Guo;Falk Hüffner;Rolf Niedermeier

  • Affiliations:

  • Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz2, D-07743Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz2, D-07743Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz2, D-07743Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz2, D-07743Jena, Germany

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2008

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Abstract

The NP-complete Closest 4-Leaf Power problem asks, given an undirected graph, whether it can be modified by at most r 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 previous work on Closest 2-Leaf Power and Closest 3-Leaf Power, we give the first algorithmic result for Closest 4-Leaf Power, showing that Closest 4-Leaf Power is fixed-parameter tractable with respect to the parameter r.