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Statements

Subject Item
n2:RIV%2F00216224%3A14330%2F09%3A00029117%21RIV11-GA0-14330___
rdf:type
skos:Concept n13:Vysledek
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 (poster) Approximating the Crossing Number of Apex Graphs (poster)
skos:prefLabel
Approximating the Crossing Number of Apex Graphs (poster) Approximating the Crossing Number of Apex Graphs (poster)
skos:notation
RIV/00216224:14330/09:00029117!RIV11-GA0-14330___
n5:aktivita
n8:S n8:P n8:Z
n5:aktivity
P(1M0545), P(GA201/08/0308), S, Z(MSM0021622419)
n5:dodaniDat
n7:2011
n5:domaciTvurceVysledku
n9:7595646
n5:druhVysledku
n6:D
n5:duvernostUdaju
n15:S
n5:entitaPredkladatele
n20:predkladatel
n5:idSjednocenehoVysledku
303920
n5:idVysledku
RIV/00216224:14330/09:00029117
n5:jazykVysledku
n22:eng
n5:klicovaSlova
crossing number; crossing minimization; apex graph
n5:klicoveSlovo
n16:crossing%20minimization n16:crossing%20number n16:apex%20graph
n5:kontrolniKodProRIV
[A976AB59598C]
n5:mistoKonaniAkce
Heraklion, Greece
n5:mistoVydani
Berlin
n5:nazevZdroje
Symposium Graph Drawing 2008, Lecture Notes in Computer Science
n5:obor
n21:IN
n5:pocetDomacichTvurcuVysledku
1
n5:pocetTvurcuVysledku
3
n5:projekt
n19:GA201%2F08%2F0308 n19:1M0545
n5:rokUplatneniVysledku
n7:2009
n5:tvurceVysledku
Mutzel, Petra Hliněný, Petr Chimani, Markus
n5:typAkce
n11:WRD
n5:wos
000264579700041
n5:zahajeniAkce
2008-10-21+02:00
n5:zamer
n18:MSM0021622419
s:issn
0302-9743
s:numberOfPages
3
n3:hasPublisher
Springer-Verlag
n14:isbn
978-3-642-00218-2
n17:organizacniJednotka
14330