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arXiv · 1904.05011

An FPT Algorithm for Max-Cut Parameterized by Crossing Number

Yasuaki Kobayashi·Yusuke Kobayashi·Shuichi Miyazaki·Suguru Tamaki
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Abstract

The Max-Cut problem is known to be NP-hard on general graphs, while it can be solved in polynomial time on planar graphs. In this paper, we present a fixed-parameter tractable algorithm for the problem on `almost' planar graphs: Given an $n$-vertex graph and its drawing with $k$ crossings, our algorithm runs in time $O(2^k(n+k)^{3/2} \log (n + k))$. Previously, Dahn, Kriege and Mutzel (IWOCA 2018) obtained an algorithm that, given an $n$-vertex graph and its $1$-planar drawing with $k$ crossings, runs in time $O(3^k n^{3/2} \log n)$. Our result simultaneously improves the running time and removes the $1$-planarity restriction.

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Yasuaki Kobayashi, Yusuke Kobayashi, Shuichi Miyazaki, Suguru Tamaki. 2019-05-24. An FPT Algorithm for Max-Cut Parameterized by Crossing Number. https://arxiv.org/abs/1904.05011

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