带最小弯曲的正交守望者路线问题的线性时间算法
A Linear-time Algorithm for Orthogonal Watchman Route Problem with Minimum Bends
摘要：
给定具有$ n $顶点的正交多边形$ P $，守望者路由问题的目标是找到$ P $中的最小长度的路径$ S $，使得多边形$ P $的每个点从$ S $的至少一个点可见。换句话说，在守望者路线问题中，我们必须计算$ n $顶点的简单多边形内的最短守望者路线，使得多边形内部及其边界上的所有点对路线上的至少一个点可见。如果路径与多边形正交，则称为正交守望者路径问题。该问题的目标之一是找到具有尽可能少的弯曲次数的正交路径。对于给定多边形为单调多边形的正交守望者路径问题，给出了一个线性时间算法。我们的算法也可用于简单正交多边形$ P $上的问题，其中由$ P $的垂直分解导出的对偶图是一条路径，称为路径多边形。
英文摘要：
Given an orthogonal polygon $ P $ with $ n $ vertices, the goal of the watchman route problem is finding a path $ S $ of the minimum length in $ P $ such that every point of the polygon $ P $ is visible from at least one of the point of $ S $. In the other words, in the watchman route problem we must compute a shortest watchman route inside a simple polygon of $ n $ vertices such that all the points interior to the polygon and on its boundary are visible to at least one point on the route. If route and polygon be orthogonal, it is called orthogonal watchman route problem. One of the targets of this problem is finding the orthogonal path with the minimum number of bends as possible. We present a linear-time algorithm for the orthogonal watchman route problem, in which the given polygon is monotone. Our algorithm can be used also for the problem on simple orthogonal polygons $ P $ for which the dual graph induced by the vertical decomposition of $ P $ is a path, which is called path polygon.
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