Fixed-Parameter Complexity of Minimum Profile Problems

  • Gregory Gutin
  • Stefan Szeider
  • Anders Yeo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4169)


An ordering of a graph G=(V,E) is a one-to-one mapping α: V →{1,2,..., |V|}. The profile of an ordering α of G is prf α (G)=∑ v ∈ V (α(v)– min {α(u): uN[v]}); here N[v] denotes the closed neighborhood of v. The profile prf(G) of G is the minimum of prf α (G) over all orderings α of G. It is well-known that prf(G) equals the minimum number of edges in an interval graph H that contains G as a subgraph. We show by reduction to a problem kernel of linear size that deciding whether the profile of a connected graph G=(V,E) is at most |V|–1+k is fixed-parameter tractable with respect to the parameter k. Since |V|–1 is a tight lower bound for the profile of a connected graph G=(V,E), the parameterization above the guaranteed value |V|–1 is of particular interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gregory Gutin
    • 1
    • 2
  • Stefan Szeider
    • 3
  • Anders Yeo
    • 1
  1. 1.Department of Computer ScienceRoyal Holloway University of LondonEgham, SurreyUnited Kingdom
  2. 2.Department of Computer ScienceUniversity of HaifaIsrael
  3. 3.Department of Computer ScienceDurham UniversityDurhamUnited Kingdom

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