Parameterised Partially-Predrawn Crossing Number

D 2022

Parameterised Partially-Predrawn Crossing Number

HAMM, Thekla and Petr HLINĚNÝ

Basic information

Original name

Parameterised Partially-Predrawn Crossing Number

Authors

HAMM, Thekla (276 Germany) and Petr HLINĚNÝ (203 Czech Republic, guarantor, belonging to the institution)

Edition

LIPIcs Vol. 224. Dagstuhl, Germany, 38th International Symposium on Computational Geometry (SoCG 2022), p. "46:1"-"46:15", 15 pp. 2022

Publisher

Schloss Dagstuhl

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

References:

DOI open access

RIV identification code

RIV/00216224:14330/22:00129306

Organization unit

Faculty of Informatics

ISBN

978-3-95977-227-3

ISSN

DOI

http://dx.doi.org/10.4230/LIPIcs.SoCG.2022.46

Keywords in English

Crossing Number; Drawing Extension; Parameterised Complexity; Partial Planarity

Abstract

V originále

Inspired by the increasingly popular research on extending partial graph drawings, we propose a new perspective on the traditional and arguably most important geometric graph parameter, the crossing number. Specifically, we define the partially predrawn crossing number to be the smallest number of crossings in any drawing of a graph, part of which is prescribed on the input (not counting the prescribed crossings). Our main result - an FPT-algorithm to compute the partially predrawn crossing number - combines advanced ideas from research on the classical crossing number and so called partial planarity in a very natural but intricate way. Not only do our techniques generalise the known FPT-algorithm by Grohe for computing the standard crossing number, they also allow us to substantially improve a number of recent parameterised results for various drawing extension problems.

Links

GA20-04567S, research and development project

Name: Struktura efektivně řešitelných případů těžkých algoritmických problémů na grafech

Investor: Czech Science Foundation

Citovat

HAMM, Thekla and Petr HLINĚNÝ. Parameterised Partially-Predrawn Crossing Number. Online. In Goaoc, Xavier and Kerber, Michael. 38th International Symposium on Computational Geometry (SoCG 2022). LIPIcs Vol. 224. Dagstuhl, Germany: Schloss Dagstuhl, 2022, p. "46:1"-"46:15", 15 pp. ISBN 978-3-95977-227-3. Available from: https://dx.doi.org/10.4230/LIPIcs.SoCG.2022.46.

@inproceedings{2243997,
   author = {Hamm, Thekla and Hliněný, Petr},
   address = {Dagstuhl, Germany},
   booktitle = {38th International Symposium on Computational Geometry (SoCG 2022)},
   doi = {http://dx.doi.org/10.4230/LIPIcs.SoCG.2022.46},
   edition = {LIPIcs Vol. 224},
   editor = {Goaoc, Xavier and Kerber, Michael},
   keywords = {Crossing Number; Drawing Extension; Parameterised Complexity; Partial Planarity},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Dagstuhl, Germany},
   isbn = {978-3-95977-227-3},
   pages = {"46:1"-"46:15"},
   publisher = {Schloss Dagstuhl},
   title = {Parameterised Partially-Predrawn Crossing Number},
   url = {http://dx.doi.org/10.4230/LIPIcs.SoCG.2022.46},
   year = {2022}
}

TY  - JOUR
ID  - 2243997
AU  - Hamm, Thekla - Hliněný, Petr
PY  - 2022
TI  - Parameterised Partially-Predrawn Crossing Number
PB  - Schloss Dagstuhl
CY  - Dagstuhl, Germany
SN  - 9783959772273
KW  - Crossing Number
KW  - Drawing Extension
KW  - Parameterised Complexity
KW  - Partial Planarity
UR  - http://dx.doi.org/10.4230/LIPIcs.SoCG.2022.46
N2  - Inspired by the increasingly popular research on extending partial graph drawings, we propose a new perspective on the traditional and arguably most important geometric graph parameter, the crossing number. Specifically, we define the partially predrawn crossing number to be the smallest number of crossings in any drawing of a graph, part of which is prescribed on the input (not counting the prescribed crossings). Our main result - an FPT-algorithm to compute the partially predrawn crossing number - combines advanced ideas from research on the classical crossing number and so called partial planarity in a very natural but intricate way. Not only do our techniques generalise the known FPT-algorithm by Grohe for computing the standard crossing number, they also allow us to substantially improve a number of recent parameterised results for various drawing extension problems.
ER  -

HAMM, Thekla and Petr HLINĚNÝ. Parameterised Partially-Predrawn Crossing Number. Online. In Goaoc, Xavier and Kerber, Michael. \textit{38th International Symposium on Computational Geometry (SoCG 2022)}. LIPIcs Vol. 224. Dagstuhl, Germany: Schloss Dagstuhl, 2022, p.~''46:1''-''46:15'', 15 pp. ISBN~978-3-95977-227-3. Available from: https://dx.doi.org/10.4230/LIPIcs.SoCG.2022.46.

Detailed Information on Publication Record