论文标题
点和多边形
Dots & Polygons
论文作者
论文摘要
我们介绍了一个新游戏，点和多边形，在平面点套装上播放。玩家轮流连接两个分，当玩家关闭A（简单）多边形时，玩家得分。我们表明，决定是否可以从给定州赢得比赛是NP-HARD。我们这样做是通过从立方平面图中的顶点 - 偶发周期堆积中减少的，包括从平面3-效应到此周期包装问题的独立降低。这也提供了一个简单的证明相关游戏点和盒子的NP硬度。对于凸位的点，我们讨论了点和多边形的贪婪策略。
We present a new game, Dots & Polygons, played on a planar point set. Players take turns connecting two points, and when a player closes a (simple) polygon, the player scores its area. We show that deciding whether the game can be won from a given state, is NP-hard. We do so by a reduction from vertex-disjoint cycle packing in cubic planar graphs, including a self-contained reduction from planar 3-Satisfiability to this cycle-packing problem. This also provides a simple proof of the NP-hardness of the related game Dots & Boxes. For points in convex position, we discuss a greedy strategy for Dots & Polygons.
