Crossing Number is Hard for Kernelization
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F16%3A00088543" target="_blank" >RIV/00216224:14330/16:00088543 - isvavai.cz</a>
Result on the web
<a href="http://socg2016.cs.tufts.edu/" target="_blank" >http://socg2016.cs.tufts.edu/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.SoCG.2016.42" target="_blank" >10.4230/LIPIcs.SoCG.2016.42</a>
Alternative languages
Result language
angličtina
Original language name
Crossing Number is Hard for Kernelization
Original language description
The graph crossing number problem, cr(G)<=k, asks for a drawing of a graph G in the plane with at most k edge crossings. Although this problem is in general notoriously difficult, it is fixed-parameter tractable for the parameter k [Grohe, STOC 2001]. This suggests a closely related question of whether this problem has a polynomial kernel, meaning whether every instance of cr(G)<=k can be in polynomial time reduced to an equivalent instance of size polynomial in k (and independent of |G|). We answer this question in the negative. Along the proof we show that the tile crossing number problem of twisted planar tiles is NP-hard, which has been an open problem for some time, too, and then employ the complexity technique of cross-composition. Our result holds already for the special case of graphs obtained from planar graphs by adding one edge.
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
<a href="/en/project/GA14-03501S" target="_blank" >GA14-03501S: Parameterized algorithms and kernelization in the context of discrete mathematics and logic</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
32nd International Symposium on Computational Geometry (SoCG 2016)
ISBN
9783959770095
ISSN
1868-8969
e-ISSN
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Number of pages
10
Pages from-to
"42:1"-"42:10"
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Place of publication
Germany
Event location
Boston, USA
Event date
Jun 14, 2016
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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