A Tighter Insertion-based Approximation of the Crossing Number

D 2011

A Tighter Insertion-based Approximation of the Crossing Number

CHIMANI, Markus a Petr HLINĚNÝ

Základní údaje

Originální název

A Tighter Insertion-based Approximation of the Crossing Number

Název česky

Přesnější aproximace průsečíkového čísla založená na vkládání

Autoři

CHIMANI, Markus (276 Německo) a Petr HLINĚNÝ (203 Česká republika, garant, domácí)

Vydání

Gremany, Automata, Languages and Programming 38th International Colloquium, ICALP 2011, od s. 122-134, 13 s. 2011

Nakladatel

Springer

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10201 Computer sciences, information science, bioinformatics

Stát vydavatele

Švýcarsko

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

tištěná verze "print"

Odkazy

DOI

Kód RIV

RIV/00216224:14330/11:00049979

Organizační jednotka

Fakulta informatiky

ISBN

978-3-642-22005-0

DOI

http://dx.doi.org/10.1007/978-3-642-22006-7_11

Klíčová slova anglicky

crossing number; crossing minimization; planar insertion

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 4. 2. 2013 12:41, prof. RNDr. Petr Hliněný, Ph.D.

Anotace

ORIG CZ

V originále

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 $|F|=1$. Hence our algorithm induces new, improved approximation bounds for the crossing number problem of $F$-almost-planar graphs, achieving constant-factor approximation for the large class of such graphs of bounded degrees and bounded size of $F$.

Česky

Podáme aproximační algoritmus pro problém vložení více hran do rovinného grafu. Toto zároveň dá nový aproximační algoritmus pro výpočet průsečíkového čísla grafu.

Návaznosti

GEGIG/11/E023, projekt VaV

Název: Kreslení grafů a jejich geometrické reprezentace (Akronym: GraDR)

Investor: Grantová agentura ČR, Graph Drawings and Representations

MSM0021622419, záměr

Název: Vysoce paralelní a distribuované výpočetní systémy

Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, Vysoce paralelní a distribuované výpočetní systémy

Citovat

CHIMANI, Markus a Petr HLINĚNÝ. A Tighter Insertion-based Approximation of the Crossing Number. In Luca Aceto, Monika Henzinger and Jirí Sgall. Automata, Languages and Programming 38th International Colloquium, ICALP 2011. Gremany: Springer, 2011, s. 122-134. ISBN 978-3-642-22005-0. Dostupné z: https://dx.doi.org/10.1007/978-3-642-22006-7_11.

@inproceedings{950102,
   author = {Chimani, Markus and Hliněný, Petr},
   address = {Gremany},
   booktitle = {Automata, Languages and Programming 38th International Colloquium, ICALP 2011},
   doi = {http://dx.doi.org/10.1007/978-3-642-22006-7_11},
   editor = {Luca Aceto, Monika Henzinger and Jirí Sgall},
   keywords = {crossing number; crossing minimization; planar insertion},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Gremany},
   isbn = {978-3-642-22005-0},
   pages = {122-134},
   publisher = {Springer},
   title = {A Tighter Insertion-based Approximation of the Crossing Number},
   url = {http://dx.doi.org/10.1007/978-3-642-22006-7_11},
   year = {2011}
}

TY  - JOUR
ID  - 950102
AU  - Chimani, Markus - Hliněný, Petr
PY  - 2011
TI  - A Tighter Insertion-based Approximation of the Crossing Number
PB  - Springer
CY  - Gremany
SN  - 9783642220050
KW  - crossing number
KW  - crossing minimization
KW  - planar insertion
UR  - http://dx.doi.org/10.1007/978-3-642-22006-7_11
L2  - http://dx.doi.org/10.1007/978-3-642-22006-7_11
N2  - 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 $|F|=1$. Hence our algorithm induces new, improved approximation bounds for the crossing number problem of $F$-almost-planar graphs, achieving constant-factor approximation for the large class of such graphs of bounded degrees and bounded size of $F$.
ER  -

CHIMANI, Markus a Petr HLINĚNÝ. A Tighter Insertion-based Approximation of the Crossing Number. In Luca Aceto, Monika Henzinger and Jirí Sgall. \textit{Automata, Languages and Programming 38th International Colloquium, ICALP 2011}. Gremany: Springer, 2011, s.~122-134. ISBN~978-3-642-22005-0. Dostupné z: https://dx.doi.org/10.1007/978-3-642-22006-7\_{}11.

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