Advertisement
Published in:
2015 | OriginalPaper | Chapter
Line Segment Covering of Cells in Arrangements
Authors : Matias Korman, Sheung-Hung Poon, Marcel Roeloffzen
Published in: Combinatorial Optimization and Applications
Publisher: Springer International Publishing
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Abstract
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.