Reference Work Entry

Encyclopedia of Optimization

pp 3676-3688

Stable Set Problem: Branch & Cut Algorithms

  • Steffen RebennackAffiliated withCenter of Applied Optimization, University of Florida

 

Article Outline

Abstract

Keywords

Introduction

Method

  Stable Set Polytope

  Separation

  Branching

  Implementation Aspects

Conclusion

See also

References

Abstract

In this article, we provide an overview on how the maximum weighted stable set problem can be solved exactly with Branch & Cut techniques. In addition, we provide selected references to other exact methods. We start with a brief introduction of the stable set problem and a few basic definitions but assuming that the reader is already familiar with the basic concepts. The main stress of this article lies in the review of polyhedral results for the stable set polytope in Sect. “Stable Set Polytope” and the discussion of separation procedures, Sect. “Separation”. An efficient Branch & Cut algorithm needs, in addition to strong separation routines, also a good branching strategy. This is discussed in Sect. “Branching”. At the end, some implementation aspects are considered.

Keywords

Stable set Independent set Maximum clique Vertex packing Branch & Cut Separation Exact method