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- W2116987769 abstract "We consider 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. We show that the minimum number of moves required to flood any given graph G is equal to the minimum, taken over all spanning trees T of G, of the number of moves required to flood T. This result is then applied to give two polynomial-time algorithms for flood-filling problems. Firstly, we can compute in polynomial time the minimum number of moves required to flood a graph with only a polynomial number of connected subgraphs. Secondly, given any coloured connected graph and a subset of the vertices of bounded size, the number of moves required to connect this subset can be computed in polynomial time." @default.
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- W2116987769 date "2012-01-01" @default.
- W2116987769 modified "2023-10-16" @default.
- W2116987769 title "Spanning Trees and the Complexity of Flood-Filling Games" @default.
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- W2116987769 doi "https://doi.org/10.1007/978-3-642-30347-0_28" @default.
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