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arXiv · 2504.12022

Hardness and Approximation Schemes for Discrete Packing and Domination

Raghunath Reddy Madireddy·Apurva Mudgal·Supantha Pandit
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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 $-1$.

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Raghunath Reddy Madireddy, Apurva Mudgal, Supantha Pandit. 2025-04-16. Hardness and Approximation Schemes for Discrete Packing and Domination. https://arxiv.org/abs/2504.12022

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