TY - JOUR
T1 - The Flood-It game parameterized by the vertex cover number
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.
AB - 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.
U2 - 10.1016/j.endm.2015.07.007
DO - 10.1016/j.endm.2015.07.007
M3 - Article
VL - 50
SP - 35
EP - 40
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
SN - 1571-0653
ER -