Solving Problems on Graphs of High Rank-Width. / Eiben, Eduard; Ganian, Robert; Szeider, Stefan.

In: Algorithmica, Vol. 80, 02.2018, p. 742–771.

Research output: Contribution to journalArticlepeer-review

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Standard

Solving Problems on Graphs of High Rank-Width. / Eiben, Eduard; Ganian, Robert; Szeider, Stefan.

In: Algorithmica, Vol. 80, 02.2018, p. 742–771.

Research output: Contribution to journalArticlepeer-review

Harvard

Eiben, E, Ganian, R & Szeider, S 2018, 'Solving Problems on Graphs of High Rank-Width', Algorithmica, vol. 80, pp. 742–771. https://doi.org/10.1007/s00453-017-0290-8

APA

Eiben, E., Ganian, R., & Szeider, S. (2018). Solving Problems on Graphs of High Rank-Width. Algorithmica, 80, 742–771. https://doi.org/10.1007/s00453-017-0290-8

Vancouver

Eiben E, Ganian R, Szeider S. Solving Problems on Graphs of High Rank-Width. Algorithmica. 2018 Feb;80:742–771. https://doi.org/10.1007/s00453-017-0290-8

Author

Eiben, Eduard ; Ganian, Robert ; Szeider, Stefan. / Solving Problems on Graphs of High Rank-Width. In: Algorithmica. 2018 ; Vol. 80. pp. 742–771.

BibTeX

@article{9a76f6c3bb5f41548272a4f881607553,
title = "Solving Problems on Graphs of High Rank-Width",
abstract = "A modulator in a graph is a vertex set whose deletion places the considered graph into some specified graph class. The cardinality of a modulator to various graph classes has long been used as a structural parameter which can be exploited to obtain fixed-parameter algorithms for a range of hard problems. Here we investigate what happens when a graph contains a modulator which is large but “well-structured” (in the sense of having bounded rank-width). Can such modulators still be exploited to obtain efficient algorithms? And is it even possible to find such modulators efficiently? We first show that the parameters derived from such well-structured modulators are more powerful for fixed-parameter algorithms than the cardinality of modulators and rank-width itself. Then, we develop a fixed-parameter algorithm for finding such well-structured modulators to every graph class which can be characterized by a finite set of forbidden induced subgraphs. We proceed by showing how well-structured modulators can be used to obtain efficient parameterized algorithms for Minimum Vertex Cover and Maximum Clique. Finally, we use the concept of well-structured modulators to develop an algorithmic meta-theorem for deciding problems expressible in monadic second order logic, and prove that this result is tight in the sense that it cannot be generalized to LinEMSO problems.",
author = "Eduard Eiben and Robert Ganian and Stefan Szeider",
year = "2018",
month = feb,
doi = "10.1007/s00453-017-0290-8",
language = "English",
volume = "80",
pages = "742–771",
journal = "Algorithmica",
issn = "0178-4617",
publisher = "Springer New York",

}

RIS

TY - JOUR

T1 - Solving Problems on Graphs of High Rank-Width

AU - Eiben, Eduard

AU - Ganian, Robert

AU - Szeider, Stefan

PY - 2018/2

Y1 - 2018/2

N2 - A modulator in a graph is a vertex set whose deletion places the considered graph into some specified graph class. The cardinality of a modulator to various graph classes has long been used as a structural parameter which can be exploited to obtain fixed-parameter algorithms for a range of hard problems. Here we investigate what happens when a graph contains a modulator which is large but “well-structured” (in the sense of having bounded rank-width). Can such modulators still be exploited to obtain efficient algorithms? And is it even possible to find such modulators efficiently? We first show that the parameters derived from such well-structured modulators are more powerful for fixed-parameter algorithms than the cardinality of modulators and rank-width itself. Then, we develop a fixed-parameter algorithm for finding such well-structured modulators to every graph class which can be characterized by a finite set of forbidden induced subgraphs. We proceed by showing how well-structured modulators can be used to obtain efficient parameterized algorithms for Minimum Vertex Cover and Maximum Clique. Finally, we use the concept of well-structured modulators to develop an algorithmic meta-theorem for deciding problems expressible in monadic second order logic, and prove that this result is tight in the sense that it cannot be generalized to LinEMSO problems.

AB - A modulator in a graph is a vertex set whose deletion places the considered graph into some specified graph class. The cardinality of a modulator to various graph classes has long been used as a structural parameter which can be exploited to obtain fixed-parameter algorithms for a range of hard problems. Here we investigate what happens when a graph contains a modulator which is large but “well-structured” (in the sense of having bounded rank-width). Can such modulators still be exploited to obtain efficient algorithms? And is it even possible to find such modulators efficiently? We first show that the parameters derived from such well-structured modulators are more powerful for fixed-parameter algorithms than the cardinality of modulators and rank-width itself. Then, we develop a fixed-parameter algorithm for finding such well-structured modulators to every graph class which can be characterized by a finite set of forbidden induced subgraphs. We proceed by showing how well-structured modulators can be used to obtain efficient parameterized algorithms for Minimum Vertex Cover and Maximum Clique. Finally, we use the concept of well-structured modulators to develop an algorithmic meta-theorem for deciding problems expressible in monadic second order logic, and prove that this result is tight in the sense that it cannot be generalized to LinEMSO problems.

U2 - 10.1007/s00453-017-0290-8

DO - 10.1007/s00453-017-0290-8

M3 - Article

VL - 80

SP - 742

EP - 771

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

ER -