Crossing Number Is NP-Hard for Constant Path-Width (And Tree-Width)

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F24%3A00139112" target="_blank" >RIV/00216224:14330/24:00139112 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.4230/LIPIcs.ISAAC.2024.40" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.ISAAC.2024.40</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ISAAC.2024.40" target="_blank" >10.4230/LIPIcs.ISAAC.2024.40</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Crossing Number Is NP-Hard for Constant Path-Width (And Tree-Width)

Popis výsledku v původním jazyce

Crossing Number is a celebrated problem in graph drawing. It is known to be NP-complete since the 1980s, and fairly involved techniques were already required to show its fixed-parameter tractability when parameterized by the vertex cover number. In this paper we prove that computing exactly the crossing number is NP-hard even for graphs of path-width 12 (and as a result, for simple graphs of path-width 13 and tree-width 9). Thus, while tree-width and path-width have been very successful tools in many graph algorithm scenarios, our result shows that general crossing number computations unlikely (under P≠ NP) could be successfully tackled using graph decompositions of bounded width, what has been a "tantalizing open problem" [S. Cabello, Hardness of Approximation for Crossing Number, 2013] till now.

Název v anglickém jazyce

Crossing Number Is NP-Hard for Constant Path-Width (And Tree-Width)

Popis výsledku anglicky

Crossing Number is a celebrated problem in graph drawing. It is known to be NP-complete since the 1980s, and fairly involved techniques were already required to show its fixed-parameter tractability when parameterized by the vertex cover number. In this paper we prove that computing exactly the crossing number is NP-hard even for graphs of path-width 12 (and as a result, for simple graphs of path-width 13 and tree-width 9). Thus, while tree-width and path-width have been very successful tools in many graph algorithm scenarios, our result shows that general crossing number computations unlikely (under P≠ NP) could be successfully tackled using graph decompositions of bounded width, what has been a "tantalizing open problem" [S. Cabello, Hardness of Approximation for Crossing Number, 2013] till now.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

35th International Symposium on Algorithms and Computation (ISAAC 2024)

ISBN

9783959773546

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

15

Strana od-do

„40:1“-„40:15“

Název nakladatele

Schloss Dagstuhl -- Leibniz-Zentrum f{"u}r Informatik

Místo vydání

Dagstuhl, Germany

Místo konání akce

Sydney, Australia

Datum konání akce

8. 12. 2024

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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