About: Planar Embeddings with Small and Uniform Faces

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Motivated by finding planar embeddings that lead to drawings with favorable aesthetics, we study the problems MinMaxFace and UniformFaces of embedding a given biconnected multi-graph such that the largest face is as small as possible and such that all faces have the same size, respectively. We prove a complexity dichotomy for MinMaxFace and show that deciding whether the maximum is at most k is polynomial-time solvable for k at most 4 and NP-complete for k at least 5. Further, we give a 6- approximation for minimizing the maximum face in a planar embedding. For UniformFaces, we show that the problem is NP-complete for odd k at least 7 and even k at least 10. Motivated by finding planar embeddings that lead to drawings with favorable aesthetics, we study the problems MinMaxFace and UniformFaces of embedding a given biconnected multi-graph such that the largest face is as small as possible and such that all faces have the same size, respectively. We prove a complexity dichotomy for MinMaxFace and show that deciding whether the maximum is at most k is polynomial-time solvable for k at most 4 and NP-complete for k at least 5. Further, we give a 6- approximation for minimizing the maximum face in a planar embedding. For UniformFaces, we show that the problem is NP-complete for odd k at least 7 and even k at least 10. (en)
Title	Planar Embeddings with Small and Uniform Faces Planar Embeddings with Small and Uniform Faces (en)
skos:prefLabel	Planar Embeddings with Small and Uniform Faces Planar Embeddings with Small and Uniform Faces (en)
skos:notation	RIV/00216208:11320/14:10282715!RIV15-GA0-11320___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GA14-14179S)
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Jelínek, Vít Kratochvíl, Jan Rutter, Ignaz
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	36732
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/14:10282715
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	approximation; complexity; Planar embedding (en)
http://linked.open.../riv/klicoveSlovo	Planar embedding approximation complexity
http://linked.open...ontrolniKodProRIV	[6B353D1FD1A0]
http://linked.open...v/mistoKonaniAkce	Jeonju, Korea
http://linked.open...i/riv/mistoVydani	Heidelberg
http://linked.open...i/riv/nazevZdroje	Algorithms and Computation : 25th International Symposium, ISAAC 2014, Jeonju, Korea, December 15-17, 2014, Proceedings
http://linked.open...in/vavai/riv/obor	IN
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Algorithmic, structural and complexity aspects of configurations in the plane
http://linked.open...UplatneniVysledku	2014
http://linked.open...iv/tvurceVysledku	Jelínek, Vít Kratochvíl, Jan Rutter, Ignaz Da Lozzo, Giordano
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2014-12-15 (xsd:date)
issn	0302-9743
number of pages	13 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/978-3-319-13075-0_50
http://purl.org/ne...btex#hasPublisher	Springer International Publishing
https://schema.org/isbn	978-3-319-13074-3
http://localhost/t...ganizacniJednotka	11320

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