# Line Segment Covering of Cells in Arrangements

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.

• 29 publications
• 1 publication
• 10 publications
research
09/26/2018

### Approximability of Covering Cells with Line Segments

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### Efficient Segment Folding is Hard

We introduce a computational origami problem which we call the segment f...
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09/26/2018

### Convex partial transversals of planar regions

We consider the problem of testing, for a given set of planar regions R...
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09/20/2019

### Corrigendum to: "Linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares", Theoretical Computer Science 769 (2019) 63--74

In the paper "Linear time algorithm to cover and hit a set of line segme...
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06/17/2022

### On Computing Optimal Linear Diagrams

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01/24/2019

### Infinite All-Layers Simple Foldability

We study the problem of deciding whether a crease pattern can be folded ...
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09/14/2017

### A linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares

This paper discusses the problem of covering and hitting a set of line s...