Maximum Cut Parameterized by Crossing Number

@article{Chimani2020MaximumCP,
  title={Maximum Cut Parameterized by Crossing Number},
  author={Markus Chimani and C. Dahn and Martina Juhnke-Kubitzke and Nils M. Kriege and Petra Mutzel and Alexander Nover},
  journal={ArXiv},
  year={2020},
  volume={abs/1903.06061}
}
  • Markus Chimani, C. Dahn, +3 authors Alexander Nover
  • Published 2020
  • Mathematics, Computer Science
  • ArXiv
  • 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 joining 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 $O(2^k \cdot p(n + k))$, where $p$ is the polynomial running time for planar Max-Cut. The only previously known similar algorithm [8] is restricted to 1… CONTINUE READING
    3 Citations
    An FPT Algorithm for Max-Cut Parameterized by Crossing Number
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    Fixed-Parameter Algorithms for the Weighted Max-Cut Problem on Embedded 1-Planar Graphs
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