Maximum cut parameterized by crossing number
Autor(en): | Chimani, M. Dahn, C. Juhnke-Kubitzke, M. Kriege, N.M. Mutzel, P. Nover, A. |
Erscheinungsdatum: | 2020 | Herausgeber: | Brown University | Enthalten in: | Journal of Graph Algorithms and Applications | Band: | 24 | Ausgabe: | 3 | Startseite: | 155 | Seitenende: | 170 | Zusammenfassung: | Given an edge-weighted graph G on n nodes, the NP-hard Max-Cut problem asks for a node bipartition such that the sum of edge weights join-ing the different partitions is maximized. We propose a fixed-parameter tractable algorithm parameterized by the number k of crossings in a given drawing of G. Our algorithm achieves a running time of O(2k · p(n k)), where p is the polynomial running time for planar Max-Cut. The only previously known similar algorithm [8] is restricted to embedded 1-planar graphs (i.e., at most one crossing per edge) and its dependency on k is of order 3k. Finally, combining this with the fact that crossing number is fixed-parameter tractable with respect to itself, we see that Max-Cut is fixed-parameter tractable with respect to the crossing number, even without a given drawing. Moreover, the results naturally carry over to the minor-monotone-version of crossing number. © 2020, Brown University. All rights reserved. |
ISSN: | 15261719 | DOI: | 10.7155/jgaa.00523 | Externe URL: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85083697028&doi=10.7155%2fjgaa.00523&partnerID=40&md5=573470a8209e3a0cabddb662c45d8fe3 |
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geprüft am 06.06.2024