On Complexity of Flooding Games on Graphs with Interval Representations

@inproceedings{Fukui2012OnCO,
  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},
  booktitle={TJJCCGG},
  year={2012}
}
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… 

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  • Graphs and Combinatorics
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References

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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

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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.

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