# An FPT algorithm for orthogonal buttons and scissors

## TL;DR

This paper presents a fixed-parameter tractable algorithm for the Buttons and Scissors puzzle, enabling efficient solutions when the number of cuts is limited, by analyzing the problem's complexity in terms of the number of cuts.

## Contribution

The paper introduces a novel fixed-parameter tractable algorithm for Buttons and Scissors based on the number of cuts, improving understanding of its computational complexity.

## Key findings

- Algorithm runs in $2^{O(k^2 \log k)} (n+m)^{O(1)}$ time
- Efficiently solves instances with bounded number of cuts
- Advances complexity analysis of puzzle games

## Abstract

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 parameterized 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.