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Polynomial kernel for Fast-Strategy parameterized by the number of guards on bipartite graphs

Develop a polynomial kernel for Fast-Strategy parameterized by the number of guards g on bipartite graphs, improving upon the fixed-parameter tractability result.

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Background

The paper proves that Fast-Strategy is fixed-parameter tractable on bipartite graphs when parameterized by the number of guards g. A natural next step in parameterized complexity is to seek polynomial kernels, which compress instances efficiently while preserving solvability.

Establishing a polynomial kernel would strengthen the parameterized tractability result and provide practical preprocessing for large instances.

References

Besides Conjecture \ref{conj-pspace-hard-bipartite}, we enumerate some open questions for future work. From a parameterized complexity perspective, we showed that Mobile-Domination-Game parameterized by the number of guards is \FPT{} on bipartite graphs. It is then natural to look for a polynomial kernel.

— Fast winning strategies for the attacker in eternal domination (2401.10584 - Bagan et al., 19 Jan 2024) in Conclusion (Open questions)