An Algorithmic Analysis of the Honey-Bee Game

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 nodes of that color that are adjacent to his own 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 outerplanar graphs. The solitaire version, where the goal is to conquer the entire graph with a minimum number of moves, is NP-hard on trees and split graphs, but can be solved in polynomial time on co-comparability graphs.

RF acknowledges support by the National Natural Science Foundation of China (No. 60973026), the Shanghai Leading Academic Discipline Project (project number B114), the Shanghai Committee of Science and Technology of China (09DZ2272800), and the Robert Bosch Foundation (Science Bridge China 32.5.8003.0040.0). GJW acknowledges support by the Netherlands Organisation for Scientific Research (NWO grant 639.033.403), and by BSIK grant 03018 (BRICKS: Basic Research in Informatics for Creating the Knowledge Society).