Weighted geometric set cover problems revisited

Weighted geometric set cover problems revisited

We study several set cover problems in low dimensional geometric settings. Specifically, we describe a PTAS for the problem of computing a minimum cover of given points by a set of weighted fat objects. Here, we allow the objects to expand by some prespecified δ-fraction of their diameter.<p>N...

Full description

Bibliographic Details
Main Authors: Sariel Har-Peled, Mira Lee
Format: Article
Language:English
Published: Carleton University 2012-05-01
Series:Journal of Computational Geometry
Online Access:http://jocg.org/index.php/jocg/article/view/77
id doaj-baba69efbd4c4c39889ebe854fb64bd2
record_format Article
spelling doaj-baba69efbd4c4c39889ebe854fb64bd22020-11-25T01:47:09ZengCarleton UniversityJournal of Computational Geometry1920-180X2012-05-013110.20382/jocg.v3i1a425Weighted geometric set cover problems revisitedSariel Har-Peled0Mira Lee1University of Illinois, Urbana-ChampaignDepartment of Computer Science; Korea Advanced Institute of Science and Technology; Gwahangno 335 Yuseong-gu; Daejeon 305-701, Republic of KoreaWe study several set cover problems in low dimensional geometric settings. Specifically, we describe a PTAS for the problem of computing a minimum cover of given points by a set of weighted fat objects. Here, we allow the objects to expand by some prespecified δ-fraction of their diameter.<p>Next, we show that the problem of computing a minimum weight cover of points by weighted halfplanes (without expansion) can be solved exactly in the plane. We also study the problem of covering ℝ<sup><em>d</em></sup> by weighted halfspaces, and provide approximation algorithms and hardness results. We also investigate the <q>dual</q>settings of computing minimum weight simplex that covers a given target point.</p><p>Finally, we provide a near linear time algorithm for the problem of solving a LP minimizing the total weight of violated constraints needed to be removed to make it feasible.</p>http://jocg.org/index.php/jocg/article/view/77
collection DOAJ
language English
format Article
sources DOAJ
author Sariel Har-Peled
Mira Lee
spellingShingle Sariel Har-Peled
Mira Lee
Weighted geometric set cover problems revisited
Journal of Computational Geometry
author_facet Sariel Har-Peled
Mira Lee
author_sort Sariel Har-Peled
title Weighted geometric set cover problems revisited
title_short Weighted geometric set cover problems revisited
title_full Weighted geometric set cover problems revisited
title_fullStr Weighted geometric set cover problems revisited
title_full_unstemmed Weighted geometric set cover problems revisited
title_sort weighted geometric set cover problems revisited
publisher Carleton University
series Journal of Computational Geometry
issn 1920-180X
publishDate 2012-05-01
description We study several set cover problems in low dimensional geometric settings. Specifically, we describe a PTAS for the problem of computing a minimum cover of given points by a set of weighted fat objects. Here, we allow the objects to expand by some prespecified δ-fraction of their diameter.<p>Next, we show that the problem of computing a minimum weight cover of points by weighted halfplanes (without expansion) can be solved exactly in the plane. We also study the problem of covering ℝ<sup><em>d</em></sup> by weighted halfspaces, and provide approximation algorithms and hardness results. We also investigate the <q>dual</q>settings of computing minimum weight simplex that covers a given target point.</p><p>Finally, we provide a near linear time algorithm for the problem of solving a LP minimizing the total weight of violated constraints needed to be removed to make it feasible.</p>
url http://jocg.org/index.php/jocg/article/view/77
work_keys_str_mv AT sarielharpeled weightedgeometricsetcoverproblemsrevisited
AT miralee weightedgeometricsetcoverproblemsrevisited
_version_ 1725015869447208960

Similar Items