Treewidth reduction for constrained separation and bipartization problems

Dániel Marx (1) , Barry O'Sullivan (2) , Igor Razgon (2)

1 TAU - Tel Aviv University
2 4C UCC - Cork Constraint Computation Centre

We present a method for reducing the treewidth of a graph while preserving all the minimal $s-t$ separators. This technique turns out to be very useful for establishing the fixed-parameter tractability of constrained separation and bipartization problems. To demonstrate the power of this technique, we prove the fixed-parameter tractability of a number of well-known separation and bipartization problems with various additional restrictions (e.g., the vertices being removed from the graph form an independent set). These results answer a number of open questions in the area of parameterized complexity.

Mots clés: fixed-parameter algorithms; graph separation problems; treewidth

Domaines: Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]

Dániel Marx, Barry O'Sullivan, Igor Razgon. Treewidth reduction for constrained separation and bipartization problems. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Inria Nancy Grand Est & Loria, Mar 2010, Nancy, France. pp.561-572. ⟨inria-00455767⟩