A Tighter Insertion-based Approximation of the Crossing Number
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F11%3A00049979" target="_blank" >RIV/00216224:14330/11:00049979 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-642-22006-7_11" target="_blank" >http://dx.doi.org/10.1007/978-3-642-22006-7_11</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-642-22006-7_11" target="_blank" >10.1007/978-3-642-22006-7_11</a>
Alternative languages
Result language
angličtina
Original language name
A Tighter Insertion-based Approximation of the Crossing Number
Original language description
Let $G$ be a planar graph and $F$ a set of additional edges not yet in $G$. The {em multiple edge insertion} problem (MEI) asks for a drawing of $G+F$ with the minimum number of pairwise edge crossings, such that the subdrawing of $G$ is plane. As an exact solution to MEI is NP-hard for general $F$, we present the first approximation algorithm for MEI which achieves an additive approximation factor (depending only on the size of $F$ and the maximum degree of $G$) in the case of connected~$G$. Our algorithm seems to be the first directly implementable one in that realm, too, next to the single edge insertion. It is also known that an (even approximate) solution to the MEI problem would approximate the crossing number of the emph{$F$-almost-planar graph} $G+F$, while computing the crossing number of $G+F$ exactly is NP-hard already when $|F|=1$.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
IN - Informatics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Automata, Languages and Programming 38th International Colloquium, ICALP 2011
ISBN
978-3-642-22005-0
ISSN
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e-ISSN
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Number of pages
13
Pages from-to
122-134
Publisher name
Springer
Place of publication
Gremany
Event location
Zurich, Switzerland
Event date
Jan 1, 2011
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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