Skip to Main content Skip to Navigation
Journal articles

An algorithmic analysis of Flood-It and Free-Flood-It on graph powers

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download

https://hal.inria.fr/hal-01188900
Contributor : Coordination Episciences Iam <>
Submitted on : Monday, August 31, 2015 - 5:03:07 PM
Last modification on : Friday, November 6, 2020 - 11:22:13 AM
Long-term archiving on: : Tuesday, December 1, 2015 - 10:41:40 AM

File

dmtcs-16-3-16.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01188900, version 1

Collections

Citation

Uéverton dos Santos Souza, Fábio Protti, Maise Silva. An algorithmic analysis of Flood-It and Free-Flood-It on graph powers. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 3 (in progress) (3), pp.279--290. ⟨hal-01188900⟩

Share

Metrics

Record views

327

Files downloads

1569