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arXiv · 1304.3653

Algorithms for Cut Problems on Trees

Iyad Kanj·Guohui Lin·Tian Liu·Weitian Tong·Ge Xia·Jinhui Xu·Boting Yang·Fenghui Zhang·Peng Zhang·Binhai Zhu
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Abstract

We study the {\sc multicut on trees} and the {\sc generalized multiway Cut on trees} problems. For the {\sc multicut on trees} problem, we present a parameterized algorithm that runs in time $O^{*}(ρ^k)$, where $ρ= \sqrt{\sqrt{2} + 1} \approx 1.555$ is the positive root of the polynomial $x^4-2x^2-1$. This improves the current-best algorithm of Chen et al. that runs in time $O^{*}(1.619^k)$. For the {\sc generalized multiway cut on trees} problem, we show that this problem is solvable in polynomial time if the number of terminal sets is fixed; this answers an open question posed in a recent paper by Liu and Zhang. By reducing the {\sc generalized multiway cut on trees} problem to the {\sc multicut on trees} problem, our results give a parameterized algorithm that solves the {\sc generalized multiway cut on trees} problem in time $O^{*}(ρ^k)$, where $ρ= \sqrt{\sqrt{2} + 1} \approx 1.555$ time.

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Iyad Kanj, Guohui Lin, Tian Liu, Weitian Tong, Ge Xia, Jinhui Xu, Boting Yang, Fenghui Zhang, Peng Zhang, Binhai Zhu. 2013-04-12. Algorithms for Cut Problems on Trees. https://arxiv.org/abs/1304.3653

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