کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4950795 | 1441033 | 2018 | 6 صفحه PDF | دانلود رایگان |
- We study a geometric version of set cover.
- Vertices are modelled as segments, edges are created via intersection.
- We show that the problem is NP-hard.
- We find an FPT algorithm and solve particular cases.
Given a collection L of line segments, we consider its arrangement and study the problem of covering all cells with line segments of L. That is, we want to find a minimum-size set Lâ² of line segments such that every cell in the arrangement has a line from Lâ² defining its boundary. We show that the problem is NP-hard, even when all segments are axis-aligned. In fact, the problem is still NP-hard when we only need to cover rectangular cells of the arrangement. For the latter problem we also show that it is fixed parameter tractable with respect to the size of the optimal solution. Finally we provide a linear time algorithm for the case where cells of the arrangement are created by recursively subdividing a rectangle using horizontal and vertical cutting segments.
Journal: Information Processing Letters - Volume 129, January 2018, Pages 25-30