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@inproceedings{1366561,
author = {Chimani, Markus and Hliněný, Petr},
address = {Germany},
booktitle = {32nd International Symposium on Computational Geometry (SoCG 2016)},
doi = {http://dx.doi.org/10.4230/LIPIcs.SoCG.2016.30},
keywords = {crossing number; crossing minimization; planar insertion},
howpublished = {elektronická verze "online"},
language = {eng},
location = {Germany},
isbn = {978-3-95977-009-5},
pages = {"30:1"-"30:15"},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
title = {Inserting Multiple Edges into a Planar Graph},
url = {http://socg2016.cs.tufts.edu/},
year = {2016}
}
TY - JOUR
ID - 1366561
AU - Chimani, Markus - Hliněný, Petr
PY - 2016
TI - Inserting Multiple Edges into a Planar Graph
PB - Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
CY - Germany
SN - 9783959770095
KW - crossing number
KW - crossing minimization
KW - planar insertion
UR - http://socg2016.cs.tufts.edu/
N2 - Let G be a connected planar (but not yet embedded) graph and F a set of additional edges not 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. An optimal solution to this problem is known to approximate the crossing number of the graph G+F. Finding an exact solution to MEI is NP-hard for general F, but linear time solvable for the special case of |F|=1 [Gutwenger et al, SODA 2001/Algorithmica] and polynomial time solvable when all of F are incident to a new vertex [Chimani et al, SODA 2009]. The complexity for general F but with constant k=|F| was open, but algorithms both with relative and absolute approximation guarantees have been presented [Chuzhoy et al, SODA 2011], [Chimani-Hlineny, ICALP 2011]. We show that the problem is fixed parameter tractable (FPT) in k for biconnected G, or if the cut vertices of G have bounded degrees. We give the first exact algorithm for this problem; it requires only O(|V(G)|) time for any constant k.
ER -
CHIMANI, Markus a Petr HLINĚNÝ. Inserting Multiple Edges into a Planar Graph. Online. In \textit{32nd International Symposium on Computational Geometry (SoCG 2016)}. Germany: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2016, s.~''30:1''-''30:15'', 15 s. ISBN~978-3-95977-009-5. Dostupné z: https://dx.doi.org/10.4230/LIPIcs.SoCG.2016.30.
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