We study the puzzle game Buttons and Scissors in which the goal is to remove all buttons from an $n\times m$ grid by a series of horizontal and vertical cuts. We show that the corresponding decision problem has an algorithm with time complexity $2^{O(k^2\log k)}+{(n+m)}^{O(1)}$, where k is an upper bound on the number of cuts.

中文翻译：

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正交按钮和剪刀的FPT算法

我们研究了益智游戏“按钮和剪刀”，其目标是从 $ñ\times 米$网格由一系列水平和垂直切割组成。我们证明了相应的决策问题具有时间复杂度的算法$2^{Ø（{ķ}^2\mathrm{日志}ķ）}+{（ñ+米）}^{Ø（\mathrm{1个}）}$，其中k是切割次数的上限。