Document Open Access Logo

A Generalization of Nemhauser and Trotter's Local Optimization Theorem

Authors Michael R. Fellows, Jiong Guo, Hannes Moser, Rolf Niedermeier

Thumbnail PDF


  • Filesize: 221 kB
  • 12 pages

Document Identifiers

Author Details

Michael R. Fellows
Jiong Guo
Hannes Moser
Rolf Niedermeier

Cite AsGet BibTex

Michael R. Fellows, Jiong Guo, Hannes Moser, and Rolf Niedermeier. A Generalization of Nemhauser and Trotter's Local Optimization Theorem. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 409-420, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)


The Nemhauser-Trotter local optimization theorem applies to the NP-hard \textsc{Vertex Cover} problem and has applications in approximation as well as parameterized algorithmics. We present a framework that generalizes Nemhauser and Trotter's result to vertex deletion and graph packing problems, introducing novel algorithmic strategies based on purely combinatorial arguments (not referring to linear programming as the Nemhauser-Trotter result originally did). We exhibit our framework using a generalization of \textsc{Vertex Cover}, called \textrm{\sc Bounded-Degree Deletion}, that has promise to become an important tool in the analysis of gene and other biological networks. For some fixed~$d\geq 0$, \textrm{\sc Bounded-Degree Deletion} asks to delete as few vertices as possible from a graph in order to transform it into a graph with maximum vertex degree at most~$d$. \textsc{Vertex Cover} is the special case of $d=0$. Our generalization of the Nemhauser-Trotter theorem implies that \textrm{\sc Bounded-Degree Deletion} has a problem kernel with a linear number of vertices for every constant~$d$. We also outline an application of our extremal combinatorial approach to the problem of packing stars with a bounded number of leaves. Finally, charting the border between (parameterized) tractability and intractability for \textrm{\sc Bounded-Degree Deletion}, we provide a W[2]-hardness result for \textrm{\sc Bounded-Degree Deletion} in case of unbounded $d$-values.
  • Algorithms
  • Computational complexity
  • NP-hard problems
  • W[2]-completeness
  • Graph problems
  • Combinatorial optimization
  • Fixed-parameter tractability
  • K


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail