An algorithmic analysis of the Honey-Bee game

The Honey-Bee game is a two-player board game that is played on a connected hexagonal colored grid or (in a generalized setting) on a connected graph with colored nodes. In a single move, a player calls a color and thereby conquers all the nodes of that color that are adjacent to his own current ter...

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Bibliographic Details
Published in:Theoretical computer science Vol. 452; pp. 75 - 87
Main Authors: Fleischer, Rudolf, Woeginger, Gerhard J.
Format: Journal Article
Language:English
Published: Elsevier B.V 21.09.2012
Subjects:
Combinatorial game
Computational complexity
Graph problem
Computational complexity
Combinatorial game
Graph problem
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:The Honey-Bee game is a two-player board game that is played on a connected hexagonal colored grid or (in a generalized setting) on a connected graph with colored nodes. In a single move, a player calls a color and thereby conquers all the nodes of that color that are adjacent to his own current territory. Both players want to conquer the majority of the nodes. We show that winning the game is PSPACE-hard in general, NP-hard on series-parallel graphs, but easy on outer-planar graphs. In the solitaire version, the goal of the single player is to conquer the entire graph with the minimum number of moves. The solitaire version is NP-hard on trees and split graphs, but can be solved in polynomial time on co-comparability graphs.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2012.05.032