کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4950795 1441033 2018 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Line segment covering of cells in arrangements
ترجمه فارسی عنوان
پوشش خط سلول ها در ترتیبات
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
چکیده انگلیسی


- 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 L′ of line segments such that every cell in the arrangement has a line from L′ 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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Information Processing Letters - Volume 129, January 2018, Pages 25-30
نویسندگان
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