Treewidth Reduction for Constrained Separation and Bipartization Problems

Authors Dániel Marx, Barry O'Sullivan, Igor Razgon



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LIPIcs.STACS.2010.2485.pdf
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Dániel Marx
Barry O'Sullivan
Igor Razgon

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Dániel Marx, Barry O'Sullivan, and Igor Razgon. Treewidth Reduction for Constrained Separation and Bipartization Problems. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 561-572, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)
https://doi.org/10.4230/LIPIcs.STACS.2010.2485

Abstract

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.
Keywords
  • Fixed-parameter algorithms
  • graph separation problems
  • treewidth

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