Extremal properties of flood-filling games

  title={Extremal properties of flood-filling games},
  author={Kitty Meeks and Dominik K. Vu},
  journal={Discret. Math. Theor. Comput. Sci.},
  • Kitty MeeksD. Vu
  • Published 2 April 2015
  • Mathematics
  • Discret. Math. Theor. Comput. Sci.
The problem of determining the number of "flooding operations" required to make a given coloured graph monochromatic in the one-player combinatorial game Flood-It has been studied extensively from an algorithmic point of view, but basic questions about the maximum number of moves that might be required in the worst case remain unanswered. We begin a systematic investigation of such questions, with the goal of determining, for a given graph, the maximum number of moves that may be required… 

Figures from this paper

A Survey on the Complexity of Flood-Filling Games

This survey, which reviews recent results on one-player flood-filling games on graphs, Flood-It and Free-Flood-It, in which the player aims to make the board monochromatic with a minimum number of flooding moves, has relevant interpretations in bioinformatics.

How Bad is the Freedom to Flood-It?

This paper investigates how freedom of choosing the vertex to play in each move affects the complexity of the problem, and shows that the length of an optimal solution for Fixed-Flood-It is always at most twice that of Free-Fl flooded, and this is tight.

Vexing Vexillological Logic

We define a new impartial combinatorial game, flag coloring , based on flood filling. We then generalize to a graph game, and find values for many positions on two colors. We demonstrate that the



The complexity of flood-filling games on graphs

Spanning Trees and the Complexity of Flood-Filling Games

Two polynomial-time algorithms for flood-filling problems related to the combinatorial game (Free-) Flood-It are considered, which 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 to flood T.

The complexity of Free-Flood-It on 2×n boards

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

This paper describes 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).

Flood-it on AT-Free Graphs

It is shown that the minimal number of moves can be computed in polynomial time when the game is played on AT-free graphs.

The Complexity of Flood Filling Games

It is shown that finding the minimum number of flooding operations is NP-hard for c≥3 and that this even holds when the player can perform flooding operations from any position on the board, and that for an unbounded number of colours, Flood-It remains NP- hard for boards of height at least 3, but is in P for board of height 2.

Parameterized Complexity of Flood-Filling Games on Trees

This work presents new results on flood-filling games, Flood-It and Free-Flood-It, in which the player aims to make the board monochromatic with a minimum number of flooding moves, and presents a general framework for reducibility from flooding problems, by defining a special graph operator ψ.

On Complexity of Flooding Games on Graphs with Interval Representations

This work investigates the one player flooding games on some graph classes characterized by interval representations and states that the number of colors is a key parameter to determine the computational complexity of the flooding games.

Flooding games on graphs