A tighter insertion-based approximation of the crossing number

J 2017

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

Autoři

CHIMANI, Markus (40 Rakousko) a Petr HLINĚNÝ (203 Česká republika, garant, domácí)

Vydání

Journal of Combinatorial Optimization, Springer, 2017, 1382-6905

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10201 Computer sciences, information science, bioinformatics

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 0.927

Kód RIV

RIV/00216224:14330/17:00094634

Organizační jednotka

Fakulta informatiky

DOI

http://dx.doi.org/10.1007/s10878-016-0030-z

UT WoS

000398945100003

Klíčová slova anglicky

Planar graph; Multiple edge insertion; SPQR tree; Crossing number

Štítky

formela-journal

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 16. 4. 2018 16:17, prof. RNDr. Petr Hliněný, Ph.D.

Anotace

V originále

Let G be a planar graph and F a set of additional edges not yet in G. The 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. Finding an exact solution to MEI is NP-hard for general F. We present the first polynomial time algorithm for MEI that achieves an additive approximation guarantee—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 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.

Návaznosti

GA14-03501S, projekt VaV

Název: Parametrizované algoritmy a kernelizace v kontextu diskrétní matematiky a logiky

Investor: Grantová agentura ČR, Parametrizované algoritmy a kernelizace v kontextu diskrétní matematiky a logiky

Citovat

CHIMANI, Markus a Petr HLINĚNÝ. A tighter insertion-based approximation of the crossing number. Journal of Combinatorial Optimization. Springer, 2017, roč. 33, č. 4, s. 1183-1225. ISSN 1382-6905. Dostupné z: https://dx.doi.org/10.1007/s10878-016-0030-z.

@article{1372354,
   author = {Chimani, Markus and Hliněný, Petr},
   article_number = {4},
   doi = {http://dx.doi.org/10.1007/s10878-016-0030-z},
   keywords = {Planar graph; Multiple edge insertion; SPQR tree; Crossing number},
   language = {eng},
   issn = {1382-6905},
   journal = {Journal of Combinatorial Optimization},
   title = {A tighter insertion-based approximation of the crossing number},
   volume = {33},
   year = {2017}
}

TY  - JOUR
ID  - 1372354
AU  - Chimani, Markus - Hliněný, Petr
PY  - 2017
TI  - A tighter insertion-based approximation of the crossing number
JF  - Journal of Combinatorial Optimization
VL  - 33
IS  - 4
SP  - 1183-1225
EP  - 1183-1225
PB  - Springer
SN  - 13826905
KW  - Planar graph
KW  - Multiple edge insertion
KW  - SPQR tree
KW  - Crossing number
N2  - Let G be a planar graph and F a set of additional edges not yet in G. The 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. Finding an exact solution to MEI is NP-hard for general F. We present the first polynomial time algorithm for MEI that achieves an additive approximation guarantee—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 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. \textit{Journal of Combinatorial Optimization}. Springer, 2017, roč.~33, č.~4, s.~1183-1225. ISSN~1382-6905. Dostupné z: https://dx.doi.org/10.1007/s10878-016-0030-z.

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