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@inproceedings{1130962,
author = {Obdržálek, Jan and Ganian, Robert},
address = {Berlin Heidelberg},
booktitle = {Combinatorial Algorithms 24th International Workshop, IWOCA 2013},
doi = {http://dx.doi.org/10.1007/978-3-642-45278-9_15},
editor = {Thierry Lecroq, Laurent Mouchard},
keywords = {MSO; model checking; vertex cover; meta-theorems; parameterized complexity},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Berlin Heidelberg},
isbn = {978-3-642-45277-2},
pages = {164-177},
publisher = {Springer},
title = {Expanding the Expressive Power of Monadic Second-Order Logic on Restricted Graph Classes},
year = {2013}
}
TY - JOUR
ID - 1130962
AU - Obdržálek, Jan - Ganian, Robert
PY - 2013
TI - Expanding the Expressive Power of Monadic Second-Order Logic on Restricted Graph Classes
PB - Springer
CY - Berlin Heidelberg
SN - 9783642452772
KW - MSO
KW - model checking
KW - vertex cover
KW - meta-theorems
KW - parameterized complexity
N2 - 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.
ER -
OBDRŽÁLEK, Jan and Robert GANIAN. Expanding the Expressive Power of Monadic Second-Order Logic on Restricted Graph Classes. In Thierry Lecroq, Laurent Mouchard. \textit{Combinatorial Algorithms 24th International Workshop, IWOCA 2013}. Berlin Heidelberg: Springer, 2013, p.~164-177. ISBN~978-3-642-45277-2. Available from: https://dx.doi.org/10.1007/978-3-642-45278-9\_{}15.
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