Exact and approximation algorithms for geometric and capacitated set cover problems
(2012) 16th Annual International Conference, COCOON 2010 In Computing and Combinatorics / Lecture Notes in Computer Science 6196. p.295310 Abstract
 First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomialtime exact solutions.
Next, we consider the following general (nonnecessarily geometric) capacitated set cover problem. There is given a set of elements with real weights and a family of sets of the elements. One can use a set if it is a subset of one of the sets in the family and the sum of the weights of its elements is at most one. The goal is to cover all the elements with the allowed sets.
We show that any polynomialtime algorithm that approximates the uncapacitated version of the set cover problem with ratio r can be converted to an... (More)  First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomialtime exact solutions.
Next, we consider the following general (nonnecessarily geometric) capacitated set cover problem. There is given a set of elements with real weights and a family of sets of the elements. One can use a set if it is a subset of one of the sets in the family and the sum of the weights of its elements is at most one. The goal is to cover all the elements with the allowed sets.
We show that any polynomialtime algorithm that approximates the uncapacitated version of the set cover problem with ratio r can be converted to an approximation algorithm for the capacitated version with ratio r + 1.357.
The composition of these two results yields a polynomialtime approximation algorithm for the problem of covering a set of customers represented by a weighted npoint set with a minimum number of antennas of variable angular range and fixed capacity with ratio 2.357. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1666081
 author
 Berman, Piotr; Karpinski, Marek and Lingas, Andrzej ^{LU}
 organization
 publishing date
 2012
 type
 Chapter in Book/Report/Conference proceeding
 publication status
 published
 subject
 in
 Computing and Combinatorics / Lecture Notes in Computer Science
 volume
 6196
 pages
 295  310
 publisher
 Springer
 conference name
 16th Annual International Conference, COCOON 2010
 external identifiers

 wos:000304695800006
 scopus:77955024653
 ISSN
 03029743
 16113349
 ISBN
 9783642140310
 DOI
 10.1007/9783642140310_26
 project
 VR 20084649
 language
 English
 LU publication?
 yes
 id
 d6d5a603c96a4372b0989b0c69ca7b1e (old id 1666081)
 date added to LUP
 20100901 14:34:48
 date last changed
 20170416 03:19:19
@inproceedings{d6d5a603c96a4372b0989b0c69ca7b1e, abstract = {First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomialtime exact solutions. <br/><br> Next, we consider the following general (nonnecessarily geometric) capacitated set cover problem. There is given a set of elements with real weights and a family of sets of the elements. One can use a set if it is a subset of one of the sets in the family and the sum of the weights of its elements is at most one. The goal is to cover all the elements with the allowed sets. <br/><br> We show that any polynomialtime algorithm that approximates the uncapacitated version of the set cover problem with ratio r can be converted to an approximation algorithm for the capacitated version with ratio r + 1.357. <br/><br> The composition of these two results yields a polynomialtime approximation algorithm for the problem of covering a set of customers represented by a weighted npoint set with a minimum number of antennas of variable angular range and fixed capacity with ratio 2.357.}, author = {Berman, Piotr and Karpinski, Marek and Lingas, Andrzej}, booktitle = {Computing and Combinatorics / Lecture Notes in Computer Science}, isbn = {9783642140310}, issn = {03029743}, language = {eng}, pages = {295310}, publisher = {Springer}, title = {Exact and approximation algorithms for geometric and capacitated set cover problems}, url = {http://dx.doi.org/10.1007/9783642140310_26}, volume = {6196}, year = {2012}, }