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Expanding the Expressive Power of Monadic Second-Order Logic on Restricted Graph Classes

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OBDRŽÁLEK Jan GANIAN Robert

Druh Článek ve sborníku
Konference Combinatorial Algorithms 24th International Workshop, IWOCA 2013
Fakulta / Pracoviště MU

Fakulta informatiky Fakulta sociálních studií

Citace
Doi http://dx.doi.org/10.1007/978-3-642-45278-9_15
Obor Informatika
Klíčová slova MSO; model checking; vertex cover; meta-theorems; parameterized complexity
Popis We combine integer linear programming and recent advances in Monadic Second-Order model checking to obtain two new algorithmic meta-theorems for graphs of bounded vertex-cover. The first one shows that the model checking problem for cardMSO1, an extension of the well-known Monadic Second-Order logic by the addition of cardinality constraints, can be solved in FPT time parameterized by vertex cover. The second meta-theorem shows that the MSO partitioning problems introduced by Rao can also be solved in FPT time with the same parameter. The significance of our contribution stems from the fact that these formalisms can describe problems which are W[1]-hard and even NP-hard on graphs of bounded tree-width. Additionally, our algorithms have only elementary dependence on the parameter and formula. We also show that both results are easily extended from vertex cover to neighborhood diversity.
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