Minimizing an Uncrossed Collection of Drawings

HLINĚNÝ, Petr a Tomáš MASAŘÍK. Minimizing an Uncrossed Collection of Drawings. Online. In Bekos, M.A., Chimani, M. Graph Drawing 2023. 14465. vyd. Switzerland: Springer, Cham, 2023, s. 110-123. ISBN 978-3-031-49271-6. Dostupné z: https://dx.doi.org/10.1007/978-3-031-49272-3_8.

Základní údaje

Originální název

Minimizing an Uncrossed Collection of Drawings

Autoři

HLINĚNÝ, Petr (203 Česká republika, garant, domácí) a Tomáš MASAŘÍK (203 Česká republika)

Vydání

14465. vyd. Switzerland, Graph Drawing 2023, od s. 110-123, 14 s. 2023

Nakladatel

Springer, Cham

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Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10201 Computer sciences, information science, bioinformatics

Stát vydavatele

Švýcarsko

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

elektronická verze "online"

Impakt faktor

Impact factor: 0.402 v roce 2005

Kód RIV

RIV/00216224:14330/23:00131579

Organizační jednotka

Fakulta informatiky

ISBN

978-3-031-49271-6

ISSN

DOI

http://dx.doi.org/10.1007/978-3-031-49272-3_8

UT WoS

001207939600008

Klíčová slova anglicky

Crossing Number; Planarity; Thickness; Fixed-parameter Tractability

Štítky

core_A, firank_A

Příznaky

Mezinárodní význam, Recenzováno

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Anotace

V originále

In this paper, we introduce the following new concept in graph drawing. Our task is to find a small collection of drawings such that they all together satisfy some property that is useful for graph visualization. We propose investigating a property where each edge is not crossed in at least one drawing in the collection. We call such collection uncrossed. This property is motivated by a quintessential problem of the crossing number, where one asks for a drawing where the number of edge crossings is minimum. Indeed, if we are allowed to visualize only one drawing, then the one which minimizes the number of crossings is probably the neatest for the first orientation. However, a collection of drawings where each highlights a different aspect of a graph without any crossings could shed even more light on the graph’s structure. We propose two definitions. First, the uncrossed number, minimizes the number of graph drawings in a collection, satisfying the uncrossed property. Second, the uncrossed crossing number, minimizes the total number of crossings in the collection that satisfy the uncrossed property. For both definitions, we establish initial results. We prove that the uncrossed crossing number is NP-hard, but there is an algorithm parameterized by the solution size.