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Exact and approximation algorithms for geometric and capacitated set cover problems

Berman, Piotr; Karpinski, Marek and Lingas, Andrzej LU (2012) 16th Annual International Conference, COCOON 2010 In Computing and Combinatorics / Lecture Notes in Computer Science 6196. p.295-310
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 polynomial-time exact solutions.

Next, we consider the following general (non-necessarily 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 polynomial-time 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 polynomial-time exact solutions.

Next, we consider the following general (non-necessarily 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 polynomial-time 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 polynomial-time approximation algorithm for the problem of covering a set of customers represented by a weighted n-point set with a minimum number of antennas of variable angular range and fixed capacity with ratio 2.357. (Less)
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author
organization
publishing date
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
0302-9743
1611-3349
ISBN
978-3-642-14031-0
DOI
10.1007/978-3-642-14031-0_26
project
VR 2008-4649
language
English
LU publication?
yes
id
d6d5a603-c96a-4372-b098-9b0c69ca7b1e (old id 1666081)
date added to LUP
2010-09-01 14:34:48
date last changed
2017-04-16 03:19:19
@inproceedings{d6d5a603-c96a-4372-b098-9b0c69ca7b1e,
  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 polynomial-time exact solutions. <br/><br>
Next, we consider the following general (non-necessarily 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 polynomial-time 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 polynomial-time approximation algorithm for the problem of covering a set of customers represented by a weighted n-point 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         = {978-3-642-14031-0},
  issn         = {0302-9743},
  language     = {eng},
  pages        = {295--310},
  publisher    = {Springer},
  title        = {Exact and approximation algorithms for geometric and capacitated set cover problems},
  url          = {http://dx.doi.org/10.1007/978-3-642-14031-0_26},
  volume       = {6196},
  year         = {2012},
}