Given a simple polygon P on n vertices, two points x , y in P are said to be visible to each other if the line segment between x and y is contained in P . The P oint G uard A rt G allery problem asks for a minimum set S such that every point in P is visible from a point in S . The V ertex G uard A rt G allery problem asks for such a set S subset of the vertices of P . A point in the set S is referred to as a guard. For both variants, we rule out any f ( k ) n o ( k / log k ) algorithm, where k := | S | is the number of guards, for any computable function f , unless the exponential time hypothesis fails. These lower bounds almost match the n O ( k ) algorithms that exist for both problems.

中文翻译：

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画廊问题的参数化硬度

给定一个简单的多边形磷在n顶点，两个点X,是的在磷如果之间的线段被认为是彼此可见的X和是的包含在磷. P软膏G警戒线一种rtG过敏问题要求最小集合小号使得每个点磷从某个点可见小号. 五号艾特克斯G警戒线一种rtG过敏问题要求这样一套小号的顶点的子集磷. 集合中的一个点小号被称为守卫。对于这两种变体，我们排除任何F(ķ)n ○(ķ/ 日志ķ)算法，其中ķ:= |小号| 是守卫的数量，对于任何可计算的功能F，除非指数时间假设失败。这些下限几乎与n ○(ķ)这两个问题都存在的算法。