The complexity of Free-Flood-It on 2xn boards

Details The complexity of Free-Flood-It on 2xn boards The complexity of Free-Flood-It on 2xn boards

2011-01-28

arxiv.org/abs/1101.5518v1

Computer Science

Data Structures and Algorithms

35 pages, 7 figures

Scientific paper

We consider the complexity of problems related to the combinatorial game Free-Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. Our main result is that computing the length of an optimal sequence is fixed parameter tractable (with the number of colours present as a parameter) when restricted to rectangular 2xn boards. We also show that, when the number of colours is unbounded, the problem remains NP-hard on such boards. This resolves a question of Clifford, Jalsenius, Montanaro and Sach (2010).

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