The Flood-It game parameterized by the vertex cover number

U.D.S. Souza; Frances Rosamond; Michael Fellows; Fabio Protti; Maise Dantas da Silva

doi:10.1016/j.endm.2015.07.007

The Flood-It game parameterized by the vertex cover number

U.D.S. Souza, Frances Rosamond, Michael Fellows, Fabio Protti, Maise Dantas da Silva

Research output: Contribution to journal › Article

Abstract

Flood-It is a combinatorial problem on a colored graph whose aim is to make the graph monochromatic using the minimum number of flooding moves, relatively to a pivot vertex p. A flooding move consists of changing the color of the monochromatic component (maximal monochromatic connected subgraph) containing p. This problem generalizes a combinatorial game named alike which is played on m×n grids. It is known that Flood-It remains NP-hard even for 3×n grids and for instances with bounded number of colors, diameter, or treewidth. In contrast, in this work we show that Flood-It is fixed-parameter tractable when parameterized by the vertex cover number, and admits a polynomial kernelization when, besides the vertex cover number, the number of colors is an additional parameter.

Original language	English
Pages (from-to)	35-40
Number of pages	6
Journal	Electronic Notes in Discrete Mathematics
Volume	50
DOIs	https://doi.org/10.1016/j.endm.2015.07.007
Publication status	Published - Dec 2015

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title = "The Flood-It game parameterized by the vertex cover number",

abstract = "Flood-It is a combinatorial problem on a colored graph whose aim is to make the graph monochromatic using the minimum number of flooding moves, relatively to a pivot vertex p. A flooding move consists of changing the color of the monochromatic component (maximal monochromatic connected subgraph) containing p. This problem generalizes a combinatorial game named alike which is played on m×n grids. It is known that Flood-It remains NP-hard even for 3×n grids and for instances with bounded number of colors, diameter, or treewidth. In contrast, in this work we show that Flood-It is fixed-parameter tractable when parameterized by the vertex cover number, and admits a polynomial kernelization when, besides the vertex cover number, the number of colors is an additional parameter.",

author = "U.D.S. Souza and Frances Rosamond and Michael Fellows and Fabio Protti and {Dantas da Silva}, Maise",

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AU - Souza, U.D.S.

AU - Rosamond, Frances

AU - Fellows, Michael

AU - Protti, Fabio

AU - Dantas da Silva, Maise

PY - 2015/12

Y1 - 2015/12

N2 - Flood-It is a combinatorial problem on a colored graph whose aim is to make the graph monochromatic using the minimum number of flooding moves, relatively to a pivot vertex p. A flooding move consists of changing the color of the monochromatic component (maximal monochromatic connected subgraph) containing p. This problem generalizes a combinatorial game named alike which is played on m×n grids. It is known that Flood-It remains NP-hard even for 3×n grids and for instances with bounded number of colors, diameter, or treewidth. In contrast, in this work we show that Flood-It is fixed-parameter tractable when parameterized by the vertex cover number, and admits a polynomial kernelization when, besides the vertex cover number, the number of colors is an additional parameter.

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