Hardness and Approximation Schemes for Discrete Packing and Domination
Computational Geometry
2025-04-17 v1
Abstract
We present polynomial-time approximation schemes based on local search} technique for both geometric (discrete) independent set (\mdis) and geometric (discrete) dominating set (\mdds) problems, where the objects are arbitrary radii disks and arbitrary side length axis-parallel squares. Further, we show that the \mdds~problem is \apx-hard for various shapes in the plane. Finally, we prove that both \mdis~and \mdds~problems are \np-hard for unit disks intersecting a horizontal line and axis-parallel unit squares intersecting a straight line with slope .
Cite
@article{arxiv.2504.12022,
title = {Hardness and Approximation Schemes for Discrete Packing and Domination},
author = {Raghunath Reddy Madireddy and Apurva Mudgal and Supantha Pandit},
journal= {arXiv preprint arXiv:2504.12022},
year = {2025}
}