On Complexity of Flooding Games on Graphs with Interval Representations

  title={On Complexity of Flooding Games on Graphs with Interval Representations},
  author={Hiroyuki Fukui and Yota Otachi and Ryuhei Uehara and Takeaki Uno and Yushi Uno},
The flooding games, which are called Flood-It, Mad Virus, or HoneyBee, are a kind of coloring games and they have been becoming popular online. In these games, each player colors one specified cell in his/her turn, and all connected neighbor cells of the same color are also colored by the color. This flooding or coloring spreads on the same color cells. It is natural to consider the coloring games on general graphs: Once a vertex is colored, the flooding flows along edges in the graph. Recently… 

Flooding games on graphs

N ov 2 01 5 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.

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.

Extremal properties of flood-filling games

This work begins a systematic investigation of the number of "flooding operations" required to make a given coloured graph monochromatic in the one-player combinatorial game Flood-It, and determines the maximum number of moves that may be required, taken over all possible colourings.

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.

Twenty Years of Progress of ${JCDCG}^3$

A summary of the notable results published in those proceedings are presented in this article and focus on six areas such as games and puzzles, dissection and reversibility, foldings and unfoldings, point sets, visibility, and geometric and topological graph theory.

Twenty Years of Progress of JCDCG3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {JCDCG}^3$$\end{document}

  • Graphs and Combinatorics
  • 2020



The complexity of flood-filling games on graphs

Flooding 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.

An algorithmic analysis of the Honey-Bee game

2-FREE-FLOOD-IT is polynomial

This report is the translation from french to english of the section in the french report showing that the variant of the problem called 2-FREE-FLOOD-IT can be solved with a polynomial algorithm, answering a question raised in the previous study of FLOODIT by Arthur et al.

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.

A Linear Time Algorithm for Deciding Interval Graph Isomorphism

It is shown that for a somewhat larger class of graphs, namely the chordal graphs, isomorphism is as hard as for general graphs.

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

Random Generation and Enumeration of Proper Interval Graphs

An enumeration algorithm of connected proper interval graphs is proposed, based on the reverse search, and it outputs eachconnected proper interval graph in $\mbox{\cal O}(1)$ time.

On Computing Longest Paths in Small Graph Classes

It is shown that the longest path problem can be solved efficiently for some tree-like graph classes by this approach, and two new graph classes that have natural interval representations are proposed.