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Statements

Subject Item
n2:RIV%2F00216224%3A14330%2F09%3A00065851%21RIV14-MSM-14330___
rdf:type
n3:Vysledek skos:Concept
rdfs:seeAlso
http://www.gd2008.org/
dcterms:description
We show that the crossing number of an apex graph, i.e.\ a graph $G$ from which only one vertex $v$ has to be removed to make it planar, can be approximated up to a factor of $\Delta(G-v)\cdot d(v)/2$ by solving the \emph{vertex inserting} problem, i.e.\ inserting a vertex plus incident edges into an optimally chosen planar embedding of a planar graph. Due to a recently developed polynomial algorithm for the latter problem, this establishes the first polynomial fixed-constant approximation algorithm for the crossing number problem of apex graphs with bounded degree. We show that the crossing number of an apex graph, i.e.\ a graph $G$ from which only one vertex $v$ has to be removed to make it planar, can be approximated up to a factor of $\Delta(G-v)\cdot d(v)/2$ by solving the \emph{vertex inserting} problem, i.e.\ inserting a vertex plus incident edges into an optimally chosen planar embedding of a planar graph. Due to a recently developed polynomial algorithm for the latter problem, this establishes the first polynomial fixed-constant approximation algorithm for the crossing number problem of apex graphs with bounded degree.
dcterms:title
Approximating the Crossing Number of Apex Graphs Approximating the Crossing Number of Apex Graphs
skos:prefLabel
Approximating the Crossing Number of Apex Graphs Approximating the Crossing Number of Apex Graphs
skos:notation
RIV/00216224:14330/09:00065851!RIV14-MSM-14330___
n4:aktivita
n12:S n12:P n12:Z
n4:aktivity
P(1M0545), P(GA201/08/0308), S, Z(MSM0021622419)
n4:dodaniDat
n14:2014
n4:domaciTvurceVysledku
n6:7595646
n4:druhVysledku
n5:D
n4:duvernostUdaju
n18:S
n4:entitaPredkladatele
n22:predkladatel
n4:idSjednocenehoVysledku
303919
n4:idVysledku
RIV/00216224:14330/09:00065851
n4:jazykVysledku
n9:eng
n4:klicovaSlova
crossing number; crossing minimization; apex graph
n4:klicoveSlovo
n15:apex%20graph n15:crossing%20minimization n15:crossing%20number
n4:kontrolniKodProRIV
[A35935C2C1BD]
n4:mistoKonaniAkce
Heraklion, Greece
n4:mistoVydani
Berlin
n4:nazevZdroje
Symposium Graph Drawing 2008, Lecture Notes in Computer Science
n4:obor
n13:IN
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
3
n4:projekt
n17:1M0545 n17:GA201%2F08%2F0308
n4:rokUplatneniVysledku
n14:2009
n4:tvurceVysledku
Chimani, Markus Mutzel, Petra Hliněný, Petr
n4:typAkce
n20:WRD
n4:wos
000264579700041
n4:zahajeniAkce
2008-10-21+02:00
n4:zamer
n24:MSM0021622419
s:issn
0302-9743
s:numberOfPages
3
n23:doi
10.1007/978-3-642-00219-9_42
n11:hasPublisher
Springer-Verlag
n19:isbn
9783642002182
n10:organizacniJednotka
14330