# Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity

@article{Chan2018StabbingRB, title={Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity}, author={Timothy M. Chan and Thomas C. van Dijk and Krzysztof Fleszar and J. Spoerhase and A. Wolff}, journal={ArXiv}, year={2018}, volume={abs/1806.02851} }

We initiate the study of the following natural geometric optimization problem. The input is a set of axis-aligned rectangles in the plane. The objective is to find a set of horizontal line segments of minimum total length so that every rectangle is stabbed by some line segment. A line segment stabs a rectangle if it intersects its left and its right boundary. The problem, which we call Stabbing, can be motivated by a resource allocation problem and has applications in geometric network design… Expand

#### 3 Citations

A QPTAS for stabbing rectangles

- Computer Science
- ArXiv
- 2021

This work presents a quasipolynomial time approximation scheme (QPTAS) for rectangle stabbing, and provides a simple 8-approximation algorithm that avoids the framework of Varadarajan. Expand

Threshold Rounding for the Standard LP Relaxation of some Geometric Stabbing Problems

- Computer Science
- ArXiv
- 2021

The rounding technique is based on a generalization of the threshold rounding idea used by Kovaleva and Spieksma, which may prove useful for rounding the LP relaxations of other geometric covering problems. Expand

Fast LP-based Approximations for Geometric Packing and Covering Problems

- Computer Science, Mathematics
- SODA
- 2020

This work derives fast approximation schemes for LP relaxations of several well-studied geometric optimization problems that include packing, covering, and mixed packing and covering constraints and obtains the first near-linear constant factor approximation algorithms for several problems. Expand

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