A Primal Approach to the Stable Set Problem

  • Claudio Gentile
  • Utz-Uwe Haus 
  • Matthias Köppe
  • Giovanni Rinaldi
  • Robert Weismantel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2461)


We present a new “primal” algorithm for the stable set problem. It is based on a purely combinatorial construction that can transform every graph into a perfect graph by replacing nodes with sets of new nodes. The transformation is done in such a way that every stable set in the perfect graph corresponds to a stable set in the original graph. The algorithm keeps a formulation of the stable set problem in a simplex-type tableau whose associated basic feasible solution is the incidence vector of the best known stable set. The combinatorial graph transformations are performed by substitutions in the generators of the feasible region. Each substitution cuts off a fractional neighbor of the current basic feasible solution. We show that “dual-type” polynomial-time separation algorithms carry over to our “primal” setting. Eventually, either a non-degenerate pivot leading to an integral basic feasible solution is performed, or the optimality of the current solution is proved.


Graph Transformation Node Variable Perfect Graph Basic Feasible Solution Nonbasic Variable 
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 2002

Authors and Affiliations

  • Claudio Gentile
    • 1
  • Utz-Uwe Haus 
    • 2
  • Matthias Köppe
    • 2
  • Giovanni Rinaldi
    • 1
  • Robert Weismantel
    • 2
  1. 1.Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”- CNRRomaItaly
  2. 2.Department of Mathematics/IMOOtto-von-Guericke-Universität MagdeburgGermany

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