Simplified Algorithmic Metatheorems Beyond MSO: Treewidth and Neighborhood Diversity

Knop, Dušan; Koutecký, Martin; Masařík, Tomáš; Toufar, Tomáš

doi:10.23638/lmcs-15(4:12)2019

Cited by 5 publications

(9 citation statements)

References 30 publications

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“…We study the linear version of the problem in [41] mentioned above; that is, the model checking of the extended MSO logic with linear local and global cardinality constraints. We show that this problem, called MSO GL Lin Model Checking, is fixed-parameter tractable parameterized by vertex integrity.…”

Section: Our Resultsmentioning

confidence: 99%

“…If one parameter is an ancestor of another, then the ancestor is upper-bounded by a function of the descendant. The fixed-parameter tractability parameterized by neighborhood diversity is shown in [41]. The W [1]-hardness parameterized by twin-cover and by treedepth and feedback vertex set number are shown in [40].…”

Section: Our Resultsmentioning

confidence: 99%

“…Knop, Koutecký, Masařík, and Toufar [41] recently converged two lines and studied the model checking of extended MSO with both local and global cardinality constraints. It is shown that the problem admits an XP algorithm parameterized by treewidth.…”

Section: Meta-theorems On Extended Mso With Cardinality Constraintsmentioning

confidence: 99%

“…We introduce an extension of MSO proposed by Knop, Koutecký, Masařík, and Toufar [41]. Let ϕ be an MSO formula with s free set variables X 1 , .…”

Section: Extensions Of Msomentioning

confidence: 99%

“…It is known that MSO GL Lin Model Checking is fixed-parameter tractable parameterized by neighborhood diversity [41], W [1]-hard parameterized by treedepth and feedback vertex set [41], and W [1]-hard parameterized by twin-cover [40].…”

Section: Mso Gl Lin Model Checking Inputmentioning

confidence: 99%

See 4 more Smart Citations

Extended MSO Model Checking via Small Vertex Integrity

Gima¹,

Otachi²

2022

Preprint

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We study the model checking problem of an extended MSO with local and global cardinality constraints, called MSO GL Lin , introduced recently by Knop, Koutecký, Masařík, and Toufar [Log. Methods Comput. Sci., 15(4), 2019]. We show that the problem is fixed-parameter tractable parameterized by vertex integrity, where vertex integrity is a graph parameter standing between vertex cover number and treedepth. Our result thus fill a gap between the fixed-parameter tractability parameterized by vertex cover number and the W[1]-hardness parameterized by treedepth.

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Section: Our Resultsmentioning

confidence: 99%