Minimizing an Uncrossed Collection of Drawings

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F23%3A00131579" target="_blank" >RIV/00216224:14330/23:00131579 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1007/978-3-031-49272-3_8" target="_blank" >http://dx.doi.org/10.1007/978-3-031-49272-3_8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-49272-3_8" target="_blank" >10.1007/978-3-031-49272-3_8</a>

Result language

angličtina

Original language name

Minimizing an Uncrossed Collection of Drawings

Original language description

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.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

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

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

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

Article name in the collection

Graph Drawing 2023

ISBN

9783031492716

ISSN

0302-9743

e-ISSN

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Number of pages

14

Pages from-to

110-123

Publisher name

Springer, Cham

Place of publication

Switzerland

Event location

Italy

Event date

Jan 1, 2023

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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