eng
Schloss Dagstuhl â Leibniz-Zentrum fĂźr Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-08-26
78:1
78:16
10.4230/LIPIcs.ESA.2020.78
article
Improved Approximation Algorithm for Set Multicover with Non-Piercing Regions
Raman, Rajiv
1
Ray, Saurabh
2
IIIT Delhi, India
NYU Abu Dhabi, United Arab Emirates
In the Set Multicover problem, we are given a set system (X,đŽ), where X is a finite ground set, and đŽ is a collection of subsets of X. Each element x â X has a non-negative demand d(x). The goal is to pick a smallest cardinality sub-collection đŽ' of đŽ such that each point is covered by at least d(x) sets from đŽ'. 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+Îľ)-approximation algorithm for the set multicover problem (P, â), where P is a set of points with demands, and â is a set of non-piercing regions, as well as for the set multicover problem (đ, P), where đ 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol173-esa2020/LIPIcs.ESA.2020.78/LIPIcs.ESA.2020.78.pdf
Approximation algorithms
geometry
Covering