License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2020.78
URN: urn:nbn:de:0030-drops-129441
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12944/
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### Improved Approximation Algorithm for Set Multicover with Non-Piercing Regions

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### Abstract

In the Set Multicover problem, we are given a set system (X,𝒮), where X is a finite ground set, and 𝒮 is a collection of subsets of X. Each element x ∈ X has a non-negative demand d(x). The goal is to pick a smallest cardinality sub-collection 𝒮' of 𝒮 such that each point is covered by at least d(x) sets from 𝒮'. In this paper, we study the set multicover problem for set systems defined by points and non-piercing regions in the plane, which includes disks, pseudodisks, k-admissible regions, squares, unit height rectangles, homothets of convex sets, upward paths on a tree, etc.
We give a polynomial time (2+ε)-approximation algorithm for the set multicover problem (P, ℛ), where P is a set of points with demands, and ℛ is a set of non-piercing regions, as well as for the set multicover problem (𝒟, P), where 𝒟 is a set of pseudodisks with demands, and P is a set of points in the plane, which is the hitting set problem with demands.

### BibTeX - Entry

```@InProceedings{raman_et_al:LIPIcs:2020:12944,
author =	{Rajiv Raman and Saurabh Ray},
title =	{{Improved Approximation Algorithm for Set Multicover with Non-Piercing Regions}},
booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
pages =	{78:1--78:16},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-162-7},
ISSN =	{1868-8969},
year =	{2020},
volume =	{173},
editor =	{Fabrizio Grandoni and Grzegorz Herman and Peter Sanders},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address =	{Dagstuhl, Germany},
URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12944},
URN =		{urn:nbn:de:0030-drops-129441},
doi =		{10.4230/LIPIcs.ESA.2020.78},
annote =	{Keywords: Approximation algorithms, geometry, Covering}
}
```

 Keywords: Approximation algorithms, geometry, Covering Collection: 28th Annual European Symposium on Algorithms (ESA 2020) Issue Date: 2020 Date of publication: 26.08.2020

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