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

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


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].


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

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