eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-30
12:1
12:14
10.4230/LIPIcs.ISAAC.2021.12
article
On Geometric Priority Set Cover Problems
Banik, Aritra
1
Raman, Rajiv
2
Ray, Saurabh
3
National Institute of Science Education and Research, HBNI, Bhubaneswar, India
Université Clermont Auvergne, Clermont Auvergne INP, CNRS, Mines Saint-Etienne, LIMOS, F-63000, Clermont-Ferrand, France
New York University, Abu Dhabi, UAE
We study the priority set cover problem for simple geometric set systems in the plane. For pseudo-halfspaces in the plane we obtain a PTAS via local search by showing that the corresponding set system admits a planar support. We show that the problem is APX-hard even for unit disks in the plane and argue that in this case the standard local search algorithm can output a solution that is arbitrarily bad compared to the optimal solution. We then present an LP-relative constant factor approximation algorithm (which also works in the weighted setting) for unit disks via quasi-uniform sampling. As a consequence we obtain a constant factor approximation for the capacitated set cover problem with unit disks. For arbitrary size disks, we show that the problem is at least as hard as the vertex cover problem in general graphs even when the disks have nearly equal sizes. We also present a few simple results for unit squares and orthants in the plane.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol212-isaac2021/LIPIcs.ISAAC.2021.12/LIPIcs.ISAAC.2021.12.pdf
Approximation algorithms
geometric set cover
local search
quasi-uniform sampling