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Parameterized Hardness of Art Gallery Problems
ACM Transactions on Algorithms ( IF 0.9 ) Pub Date : 2020-06-22 , DOI: 10.1145/3398684 Édouard Bonnet 1 , Tillmann Miltzow 2
ACM Transactions on Algorithms ( IF 0.9 ) Pub Date : 2020-06-22 , DOI: 10.1145/3398684 Édouard Bonnet 1 , Tillmann Miltzow 2
Affiliation
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:
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rt G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rt G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。
更新日期:2020-06-22
中文翻译:
画廊问题的参数化硬度
给定一个简单的多边形