在线探索简单三角形和六角形网格多边形
Exploring Simple Triangular and Hexagonal Grid Polygons Online
摘要：
我们研究了移动机器人在一个未知的细胞环境中移动的近视眼的在线探索问题（又名覆盖）的六边形和三角形作为类型的细胞。要探索一个单元格，机器人必须进入它。一旦进入，机器人就知道3个或6个相邻单元格中的哪一个存在，哪些是边界边缘。机器人的任务是访问给定环境中的每个细胞并返回到起点。我们的兴趣是在一个短的探索之旅，也就是说，在保持多个细胞访问的数量小。对于不含障碍物的任意环境，我们提供了一种策略，对于六边形网格，产生长度S <= C + 1/4 E - 2.5的旅行，对于三角形网格，产生长度S <= C + E - 4的旅行。C表示给定环境的单元格数（区域），E表示给定环境的边界边数（周长）。此外，我们表明，我们的策略是4/3竞争力在这两种类型的网格，我们提供了14/13的六边形网格和7/6三角形网格的下限。
英文摘要：
We investigate the online exploration problem (aka covering) of a short-sighted mobile robot moving in an unknown cellular environment with hexagons and triangles as types of cells. To explore a cell, the robot must enter it. Once inside, the robot knows which of the 3 or 6 adjacent cells exist and which are boundary edges. The robot's task is to visit every cell in the given environment and to return to the start. Our interest is in a short exploration tour; that is, in keeping the number of multiple cell visits small. For arbitrary environments containing no obstacles we provide a strategy producing tours of length S <= C + 1/4 E - 2.5 for hexagonal grids, and S <= C + E - 4 for triangular grids. C denotes the number of cells-the area-, E denotes the number of boundary edges-the perimeter-of the given environment. Further, we show that our strategy is 4/3-competitive in both types of grids, and we provide lower bounds of 14/13 for hexagonal grids and 7/6 for triangular grids.
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