An algorithmic analysis of the Honey-Bee game

Authors:
Rudolf Fleischer;Gerhard J. Woeginger
Affiliations:
SCS and IIPL, Fudan University, Shanghai, China and GUtech, Muscat, Oman;Department of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

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.