research-article

Geometric packing under non-uniform constraints

Authors:

Sariel Har-Peled,

Benjamin RaichelAuthors Info & Claims

SoCG '12: Proceedings of the twenty-eighth annual symposium on Computational geometry

Pages 11 - 20

https://doi.org/10.1145/2261250.2261253

Published: 17 June 2012 Publication History

Abstract

We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity. We provide a general framework and an algorithm for approximating the optimal solution for packing in hypergraphs arising out of such geometric settings. Using this framework we get a flotilla of results on this problem (and also on its dual, where one wants to pick a maximum weight subset of the points when the regions have capacities). For example, for the case of fat triangles of similar size, we show an (1)-approximation and prove that no PTAS is possible. See [ehr-gpnuc-11] for the full version of the paper.

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Cited By

Jartoux BMustafa N(2022)A Tight Analysis of Geometric Local SearchDiscrete & Computational Geometry10.1007/s00454-021-00343-yOnline publication date: 15-Jan-2022
https://doi.org/10.1007/s00454-021-00343-y
Raman RRay S(2020)Constructing Planar Support for Non-Piercing RegionsDiscrete & Computational Geometry10.1007/s00454-020-00216-wOnline publication date: 22-Jun-2020
https://doi.org/10.1007/s00454-020-00216-w
Adamaszek AHar-Peled SWiese A(2019)Approximation Schemes for Independent Set and Sparse Subsets of PolygonsJournal of the ACM10.1145/332612266:4(1-40)Online publication date: 17-Jun-2019
https://dl.acm.org/doi/10.1145/3326122
Show More Cited By

Index Terms

Geometric packing under non-uniform constraints
1. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

SoCG '12: Proceedings of the twenty-eighth annual symposium on Computational geometry

June 2012

436 pages

ISBN:9781450312998

DOI:10.1145/2261250

Program Chairs:
Tamal Dey
The Ohio State University, USA
,
Sue Whitesides
University of Victoria, Canada

Copyright © 2012 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 17 June 2012

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SoCG '12: Symposium on Computational Geometry 2012

June 17 - 20, 2012

North Carolina, Chapel Hill, USA

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

Jartoux BMustafa N(2022)A Tight Analysis of Geometric Local SearchDiscrete & Computational Geometry10.1007/s00454-021-00343-yOnline publication date: 15-Jan-2022
https://doi.org/10.1007/s00454-021-00343-y
Raman RRay S(2020)Constructing Planar Support for Non-Piercing RegionsDiscrete & Computational Geometry10.1007/s00454-020-00216-wOnline publication date: 22-Jun-2020
https://doi.org/10.1007/s00454-020-00216-w
Adamaszek AHar-Peled SWiese A(2019)Approximation Schemes for Independent Set and Sparse Subsets of PolygonsJournal of the ACM10.1145/332612266:4(1-40)Online publication date: 17-Jun-2019
https://dl.acm.org/doi/10.1145/3326122
Ashok PBasu Roy AGovindarajan S(2019)Local search strikes again: PTAS for variants of geometric covering and packingJournal of Combinatorial Optimization10.1007/s10878-019-00432-yOnline publication date: 21-Jun-2019
https://doi.org/10.1007/s10878-019-00432-y
Basu Roy AGovindarajan SRaman RRay S(2018)Packing and Covering with Non-Piercing RegionsDiscrete & Computational Geometry10.1007/s00454-018-9983-260:2(471-492)Online publication date: 1-Sep-2018
https://dl.acm.org/doi/10.1007/s00454-018-9983-2
Ashok PBasu Roy AGovindarajan S(2017)Local Search Strikes Again: PTAS for Variants of Geometric Covering and PackingComputing and Combinatorics10.1007/978-3-319-62389-4_3(25-37)Online publication date: 1-Jul-2017
https://doi.org/10.1007/978-3-319-62389-4_3
Har-Peled SIndyk PMahabadi SVakilian AMilo TTan W(2016)Towards Tight Bounds for the Streaming Set Cover ProblemProceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/2902251.2902287(371-383)Online publication date: 15-Jun-2016
https://dl.acm.org/doi/10.1145/2902251.2902287
Har-Peled SCheng SDevillers O(2014)Quasi-Polynomial Time Approximation Scheme for Sparse Subsets of PolygonsProceedings of the thirtieth annual symposium on Computational geometry10.1145/2582112.2582157(120-129)Online publication date: 8-Jun-2014
https://dl.acm.org/doi/10.1145/2582112.2582157
Ezra Eda Fonseca GLewiner TPeñaranda LChan TKlein R(2013)Small-size relative (p,ε)-approximations for well-behaved range spacesProceedings of the twenty-ninth annual symposium on Computational geometry10.1145/2462356.2462363(233-242)Online publication date: 17-Jun-2013
https://dl.acm.org/doi/10.1145/2462356.2462363
Chan TDey TWhitesides S(2012)Conflict-free coloring of points with respect to rectangles and approximation algorithms for discrete independent setProceedings of the twenty-eighth annual symposium on Computational geometry10.1145/2261250.2261293(293-302)Online publication date: 17-Jun-2012
https://dl.acm.org/doi/10.1145/2261250.2261293

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