Treewidth Reduction for Constrained Separation and Bipartization Problems

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 in the design of parameterized algorithms. We prove the fixed-parameter tractability of the s−t Cut, Multicut, and Bipartization problems (parameterized by the maximal number k of vertices being removed) 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.

• Type: Conference
• Year: 2010
• Where: STACS
• Authors: Dániel Marx, Barry O'Sullivan, Igor Razgon
• Keywords: Minimal S−t Separators, Parameterized Algorithms, STACS 2010, Theoretical Computer Science, Various Additional Restrictions