Linear-Time Algorithms for Graphs of Bounded Rankwidth: A Fresh Look Using Game Theory

(Extended Abstract)
• Alexander Langer
• Peter Rossmanith
• Somnath Sikdar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6648)

Abstract

We present an alternative proof of a theorem by Courcelle, Makowski and Rotics [6] which states that problems expressible in MSO1 are solvable in linear time for graphs of bounded rankwidth. Our proof uses a game-theoretic approach and has the advantage of being self-contained. In particular, our presentation does not assume any background in logic or automata theory. Moreover our approach can be generalized to prove other results of a similar flavor, for example, that of Courcelle’s Theorem for treewidth [3,19].

Keywords

Characteristic Tree Free Variable Parse Tree Winning Strategy Relation Symbol
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

• Alexander Langer
• 1
• Peter Rossmanith
• 1
• Somnath Sikdar
• 1
1. 1.RWTH Aachen UniversityAachenGermany