Linear-time algorithms for graphs of bounded rankwidt: a fresh look using game theory

Authors:
Alexander Langer;Peter Rossmanith;Somnath Sikdar
Affiliations:
RWTH Aachen University, Aachen, Germany;RWTH Aachen University, Aachen, Germany;RWTH Aachen University, Aachen, Germany
Venue:
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Year:
2011

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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 selfcontained. 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].