Document

**Published in:** LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Recently, Brand, Ganian and Simonov introduced a parameterized refinement of the classical PAC-learning sample complexity framework. A crucial outcome of their investigation is that for a very wide range of learning problems, there is a direct and provable correspondence between fixed-parameter PAC-learnability (in the sample complexity setting) and the fixed-parameter tractability of a corresponding "consistency checking" search problem (in the setting of computational complexity). The latter can be seen as generalizations of classical search problems where instead of receiving a single instance, one receives multiple yes- and no-examples and is tasked with finding a solution which is consistent with the provided examples.
Apart from a few initial results, consistency checking problems are almost entirely unexplored from a parameterized complexity perspective. In this article, we provide an overview of these problems and their connection to parameterized sample complexity, with the primary aim of facilitating further research in this direction. Afterwards, we establish the fixed-parameter (in)-tractability for some of the arguably most natural consistency checking problems on graphs, and show that their complexity-theoretic behavior is surprisingly very different from that of classical decision problems. Our new results cover consistency checking variants of problems as diverse as (k-)Path, Matching, 2-Coloring, Independent Set and Dominating Set, among others.

Robert Ganian, Liana Khazaliya, and Kirill Simonov. Consistency Checking Problems: A Gateway to Parameterized Sample Complexity. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{ganian_et_al:LIPIcs.IPEC.2023.18, author = {Ganian, Robert and Khazaliya, Liana and Simonov, Kirill}, title = {{Consistency Checking Problems: A Gateway to Parameterized Sample Complexity}}, booktitle = {18th International Symposium on Parameterized and Exact Computation (IPEC 2023)}, pages = {18:1--18:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-305-8}, ISSN = {1868-8969}, year = {2023}, volume = {285}, editor = {Misra, Neeldhara and Wahlstr\"{o}m, Magnus}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.18}, URN = {urn:nbn:de:0030-drops-194374}, doi = {10.4230/LIPIcs.IPEC.2023.18}, annote = {Keywords: consistency checking, sample complexity, fixed-parameter tractability} }

Document

**Published in:** LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

The problem of deciding whether a biconnected planar digraph G = (V,E) can be augmented to become an st-planar graph by adding a set of oriented edges E' ⊆ V × V is known to be NP-complete. We show that the problem is fixed-parameter tractable when parameterized by the size of the set E'.

Liana Khazaliya, Philipp Kindermann, Giuseppe Liotta, Fabrizio Montecchiani, and Kirill Simonov. The st-Planar Edge Completion Problem Is Fixed-Parameter Tractable. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 46:1-46:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{khazaliya_et_al:LIPIcs.ISAAC.2023.46, author = {Khazaliya, Liana and Kindermann, Philipp and Liotta, Giuseppe and Montecchiani, Fabrizio and Simonov, Kirill}, title = {{The st-Planar Edge Completion Problem Is Fixed-Parameter Tractable}}, booktitle = {34th International Symposium on Algorithms and Computation (ISAAC 2023)}, pages = {46:1--46:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-289-1}, ISSN = {1868-8969}, year = {2023}, volume = {283}, editor = {Iwata, Satoru and Kakimura, Naonori}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.46}, URN = {urn:nbn:de:0030-drops-193483}, doi = {10.4230/LIPIcs.ISAAC.2023.46}, annote = {Keywords: st-planar graphs, parameterized complexity, upward planarity} }

Document

**Published in:** Dagstuhl Reports, Volume 13, Issue 4 (2023)

This report documents the program and the outcomes of Dagstuhl Seminar 23162 "New Frontiers of Parameterized Complexity in Graph Drawing”. The seminar was held in-person from April 16 to April 21, 2023. It brought together 32 researchers from the Graph Drawing and the Parameterized Complexity research communities to discuss and explore new research frontiers on the interface between the two fields. The report collects the abstracts of talks and open problems presented in the seminar, as well as brief progress reports from the working groups.

Robert Ganian, Fabrizio Montecchiani, Martin Nöllenburg, Meirav Zehavi, and Liana Khazaliya. New Frontiers of Parameterized Complexity in Graph Drawing (Dagstuhl Seminar 23162). In Dagstuhl Reports, Volume 13, Issue 4, pp. 58-97, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@Article{ganian_et_al:DagRep.13.4.58, author = {Ganian, Robert and Montecchiani, Fabrizio and N\"{o}llenburg, Martin and Zehavi, Meirav and Khazaliya, Liana}, title = {{New Frontiers of Parameterized Complexity in Graph Drawing (Dagstuhl Seminar 23162)}}, pages = {58--97}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2023}, volume = {13}, number = {4}, editor = {Ganian, Robert and Montecchiani, Fabrizio and N\"{o}llenburg, Martin and Zehavi, Meirav and Khazaliya, Liana}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.13.4.58}, URN = {urn:nbn:de:0030-drops-192393}, doi = {10.4230/DagRep.13.4.58}, annote = {Keywords: algorithm design, computational geometry, graph drawing, parameterized complexity} }

Document

**Published in:** LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for fundamental representations such as planar and beyond-planar topological drawings. In this paper, we consider the extension problem for bend-minimal orthogonal drawings of planar graphs, which is among the most fundamental geometric graph drawing representations. While the problem was known to be NP-hard, it is natural to consider the case where only a small part of the graph is still to be drawn. Here, we establish the fixed-parameter tractability of the problem when parameterized by the size of the missing subgraph. Our algorithm is based on multiple novel ingredients which intertwine geometric and combinatorial arguments. These include the identification of a new graph representation of bend-equivalent regions for vertex placement in the plane, establishing a bound on the treewidth of this auxiliary graph, and a global point-grid that allows us to discretize the possible placement of bends and vertices into locally bounded subgrids for each of the above regions.

Sujoy Bhore, Robert Ganian, Liana Khazaliya, Fabrizio Montecchiani, and Martin Nöllenburg. Extending Orthogonal Planar Graph Drawings Is Fixed-Parameter Tractable. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{bhore_et_al:LIPIcs.SoCG.2023.18, author = {Bhore, Sujoy and Ganian, Robert and Khazaliya, Liana and Montecchiani, Fabrizio and N\"{o}llenburg, Martin}, title = {{Extending Orthogonal Planar Graph Drawings Is Fixed-Parameter Tractable}}, booktitle = {39th International Symposium on Computational Geometry (SoCG 2023)}, pages = {18:1--18:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-273-0}, ISSN = {1868-8969}, year = {2023}, volume = {258}, editor = {Chambers, Erin W. and Gudmundsson, Joachim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.18}, URN = {urn:nbn:de:0030-drops-178689}, doi = {10.4230/LIPIcs.SoCG.2023.18}, annote = {Keywords: orthogonal drawings, bend minimization, extension problems, parameterized complexity} }

Document

**Published in:** LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

For a graph G, a subset S ⊆ V(G) is called a resolving set if for any two vertices u,v ∈ V(G), there exists a vertex w ∈ S such that d(w,u) ≠ d(w,v). The Metric Dimension problem takes as input a graph G and a positive integer k, and asks whether there exists a resolving set of size at most k. This problem was introduced in the 1970s and is known to be NP-hard [GT 61 in Garey and Johnson’s book]. In the realm of parameterized complexity, Hartung and Nichterlein [CCC 2013] proved that the problem is W[2]-hard when parameterized by the natural parameter k. They also observed that it is FPT when parameterized by the vertex cover number and asked about its complexity under smaller parameters, in particular the feedback vertex set number. We answer this question by proving that Metric Dimension is W[1]-hard when parameterized by the feedback vertex set number. This also improves the result of Bonnet and Purohit [IPEC 2019] which states that the problem is W[1]-hard parameterized by the treewidth. Regarding the parameterization by the vertex cover number, we prove that Metric Dimension does not admit a polynomial kernel under this parameterization unless NP ⊆ coNP/poly. We observe that a similar result holds when the parameter is the distance to clique. On the positive side, we show that Metric Dimension is FPT when parameterized by either the distance to cluster or the distance to co-cluster, both of which are smaller parameters than the vertex cover number.

Esther Galby, Liana Khazaliya, Fionn Mc Inerney, Roohani Sharma, and Prafullkumar Tale. Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 51:1-51:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{galby_et_al:LIPIcs.MFCS.2022.51, author = {Galby, Esther and Khazaliya, Liana and Mc Inerney, Fionn and Sharma, Roohani and Tale, Prafullkumar}, title = {{Metric Dimension Parameterized by Feedback Vertex Set and Other Structural Parameters}}, booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)}, pages = {51:1--51:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-256-3}, ISSN = {1868-8969}, year = {2022}, volume = {241}, editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.51}, URN = {urn:nbn:de:0030-drops-168496}, doi = {10.4230/LIPIcs.MFCS.2022.51}, annote = {Keywords: Metric Dimension, Parameterized Complexity, Feedback Vertex Set} }

X

Feedback for Dagstuhl Publishing

Feedback submitted

Please try again later or send an E-mail