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  • 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.
  • 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. (en)
Title
  • Expanding the Expressive Power of Monadic Second-Order Logic on Restricted Graph Classes
  • Expanding the Expressive Power of Monadic Second-Order Logic on Restricted Graph Classes (en)
skos:prefLabel
  • Expanding the Expressive Power of Monadic Second-Order Logic on Restricted Graph Classes
  • Expanding the Expressive Power of Monadic Second-Order Logic on Restricted Graph Classes (en)
skos:notation
  • RIV/00216224:14330/13:00066545!RIV14-GA0-14330___
http://linked.open...avai/predkladatel
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GAP202/11/0196)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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  • 73949
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14330/13:00066545
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • MSO; model checking; vertex cover; meta-theorems; parameterized complexity (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [101D95EA52D4]
http://linked.open...v/mistoKonaniAkce
  • Rouen, France
http://linked.open...i/riv/mistoVydani
  • Berlin Heidelberg
http://linked.open...i/riv/nazevZdroje
  • Combinatorial Algorithms 24th International Workshop, IWOCA 2013
http://linked.open...in/vavai/riv/obor
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http://linked.open...vavai/riv/projekt
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http://linked.open...iv/tvurceVysledku
  • Ganian, Robert
  • Obdržálek, Jan
http://linked.open...vavai/riv/typAkce
http://linked.open.../riv/zahajeniAkce
issn
  • 0302-9743
number of pages
http://bibframe.org/vocab/doi
  • 10.1007/978-3-642-45278-9_15
http://purl.org/ne...btex#hasPublisher
  • Springer-Verlag
https://schema.org/isbn
  • 9783642452772
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  • 14330
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