Uéverton dos Santos Souza ; Fábio Protti ; Maise Silva - An algorithmic analysis of Flood-It and Free-Flood-It on graph powers

dmtcs:2086 - Discrete Mathematics & Theoretical Computer Science, December 14, 2014, Vol. 16 no. 3 - https://doi.org/10.46298/dmtcs.2086
An algorithmic analysis of Flood-It and Free-Flood-It on graph powersArticle

Authors: Uéverton dos Santos Souza ORCID1,2,3; Fábio Protti 2; Maise Silva 4

Flood-it is a combinatorial game played on a colored graph G whose aim is to make the graph monochromatic using the minimum number of flooding moves, relatively to a fixed pivot. Free-Flood-it is a variant where the pivot can be freely chosen for each move of the game. The standard versions of Flood-it and Free-Flood-it are played on m ×n grids. In this paper we analyze the behavior of these games when played on other classes of graphs, such as d-boards, powers of cycles and circular grids. We describe polynomial time algorithms to play Flood-it on C2n (the second power of a cycle on n vertices), 2 ×n circular grids, and some types of d-boards (grids with a monochromatic column). We also show that Free-Flood-it is NP-hard on C2n and 2 ×n circular grids.

Volume: Vol. 16 no. 3
Section: Analysis of Algorithms
Published on: December 14, 2014
Submitted on: June 27, 2014
Keywords: Combinatorial Games,Graph algorithms,Computational Complexity,Flood-it,Free-Flood-it,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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