关于用单位间隔覆盖分段

Dan Bergren, E. Eiben, R. Ganian, Iyad A. Kanj
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引用次数: 1

摘要

我们研究了用最小数量的单位长度区间覆盖直线上的一组线段的问题,其中如果线段的两个端点中至少有一个落在单位区间内,则区间覆盖线段。我们还研究了这个问题的几个变体。我们证明了上述问题对所有片段具有相同长度的实例集的限制是np困难的。这一结果暗示了文献中对所考虑的问题的变体和推广的几个np -硬度结果。然后研究了上述问题的参数化复杂度。我们通过表明它们对于所有片段具有相同长度的限制是固定参数可处理的,并且在其他情况下是W[1]完全的,从而为它们中的大多数提供了紧密的结果。2012 ACM学科分类计算理论→参数化复杂度与精确算法;计算理论→计算几何
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On Covering Segments with Unit Intervals
We study the problem of covering a set of segments on a line with the minimum number of unit-length intervals, where an interval covers a segment if at least one of the two endpoints of the segment falls in the unit interval. We also study several variants of this problem. We show that the restrictions of the aforementioned problems to the set of instances in which all the segments have the same length are NP-hard. This result implies several NP-hardness results in the literature for variants and generalizations of the problems under consideration. We then study the parameterized complexity of the aforementioned problems. We provide tight results for most of them by showing that they are fixed-parameter tractable for the restrictions in which all the segments have the same length, and are W[1]-complete otherwise. 2012 ACM Subject Classification Theory of computation → Parameterized complexity and exact algorithms; Theory of computation → Computational geometry
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