R. Ganian, J. Obdrálek:

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

Talk: International Workshop on Combinatorial Algorithms (IWOCA), Rouen, France; 2013-07-10 - 2013-07-12; in: "Combinatorial Algorithms - 24th International Workshop", T. Lecroq, L. Mouchard (ed.); Springer / LNCS, 8288 (2013), ISBN: 978-3-642-45277-2; 164 - 177.

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.

MSO model checking, parameterized complexity, vertex cover, integer linear programming

Project Head Stefan Szeider:

The Parameterized Complexity of Reasoning Problems

Created from the Publication Database of the Vienna University of Technology.