A simple quadratic kernel for Token Jumping on surfaces
Abstract
The problem \textsc{Token Jumping} asks whether, given a graph $G$ and two independent sets of \emph{tokens} $I$ and $J$ of $G$, we can transform $I$ into $J$ by changing the position of a single token in each step and having an independent set of tokens throughout. We show that there is a polynomial-time algorithm that, given an instance of \textsc{Token Jumping}, computes an equivalent instance of size $O(g^2 + gk + k^2)$, where $g$ is the genus of the input graph and $k$ is the size of the independent sets.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.04743
- arXiv:
- arXiv:2408.04743
- Bibcode:
- 2024arXiv240804743C
- Keywords:
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- Computer Science - Data Structures and Algorithms;
- Computer Science - Discrete Mathematics;
- 05C85;
- 05C69
- E-Print:
- 11 pages, 1 figure