Govindarajan, S and Sarkar, S (2024) Improved Algorithms for Minimum-Membership Geometric Set Cover. In: UNSPECIFIED, pp. 103-116.
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Abstract
Bandyapadhyay et al. introduced the generalized minimum-membership geometric set cover (GMMGSC) problem SoCG, 2023, which is defined as follows: We are given two sets P and P� of points in R2, n= max (| P|, | P�| ), and a set S of m axis-parallel unit squares. The goal is to find a subset S�� S that covers all the points in P while minimizing memb(P�, S�), where memb(P�,S�)=maxp�P�|{s�S�:p�s}|. We study GMMGSC problem and give a 16-approximation algorithm that runs in O(m2log m+ m2n) time. Our result is a significant improvement to the 144-approximation given by Bandyapadhyay et al. that runs in O~ (nm) time. GMMGSC problem is a generalization of another well-studied problem called Minimum Ply Geometric Set Cover (MPGSC), in which the goal is to minimize the ply of S�, where the ply is the maximum cardinality of a subset of the unit squares that have a non-empty intersection. The best-known result for the MPGSC problem is an 8-approximation algorithm by Durocher et al. that runs in O(n+ m8k4log k+ m8log mlog k) time, where k is the optimal ply value WALCOM, 2023. © 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.
| Item Type: | Conference Paper |
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| Publication: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to Author. |
| Keywords: | Computational geometry, Cardinalities; Generalisation; Geometric sets; Improved * algorithm; Minimum ply covering; Minimum-membership geometric set cover; Non-empty intersections; Set cover problem; Set-cover; Unit squares, Approximation algorithms |
| Department/Centre: | Division of Information Sciences (Doesn't exist now) > BioInformatics Centre |
| Date Deposited: | 04 Mar 2024 07:04 |
| Last Modified: | 04 Mar 2024 07:04 |
| URI: | https://eprints.iisc.ac.in/id/eprint/84183 |
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