蜜蜂游戏的数学分析
An Algorithmic Analysis of the Honey-Bee Game
摘要：
蜜蜂游戏是一个两人棋盘游戏，在一个连接的六边形彩色网格上或（在一般化的设置中）在一个有彩色节点的连接图上进行。在一次移动中，玩家调用一种颜色，从而征服与他自己当前领土相邻的该颜色的所有节点。两个参与人都想征服大多数节点。我们表明，赢得比赛是PSPACE-硬的一般情况下，NP-难的串-平行图，但容易外平面图。在单人纸牌游戏中，单人玩家的目标是用最少的移动次数征服整个图。Solitaire版本在树和分裂图上是NP-难的，但可以在多项式时间内在可比较图上求解。
英文摘要：
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 outerplanar 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
