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Proceedings Article, Paper
@InProceedings
Beitrag in Tagungsband, Workshop

Author, Editor
Author(s):
Fekete, Sándor P.
Friedrichs, Stephan
Kröller, Alexander
Schmidt, Christiane
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dblp
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Not MPG Author(s):
Fekete, Sándor P.
Friedrichs, Stephan
Kröller, Alexander
Schmidt, Christiane
Editor(s):
Du, Ding-Zhu
Zhang, Guochuan
dblp
dblp
Not MPII Editor(s):
Du, Ding-Zhu
Zhang, Guochuan
BibTeX cite key*:
ffks-ffagp-13
Title, Booktitle
Title*:
Facets for Art Gallery Problems
Booktitle*:
Computing and Combinatorics
Event, URLs
Conference URL::
http://www.cs.zju.edu.cn/algo/cocoon2013/
Downloading URL:
Event Address*:
Hangzhou, China
Language:
English
Event Date*
(no longer used):
Organization:
Event Start Date:
21 June 2013
Event End Date:
23 June 2013
Publisher
Name*:
Springer
URL:
http://www.springer.com/
Address*:
Berlin
Type:
Vol, No, Year, pp.
Series:
Lecture Notes in Computer Science
Volume:
7936
Number:
Month:
June
Pages:
208-220
Year*:
2013
VG Wort Pages:
ISBN/ISSN:
978-3-642-38767-8
Sequence Number:
DOI:
10.1007/978-3-642-38768-5_20
Note, Abstract, ©
(LaTeX) Abstract:
We demonstrate how polyhedral methods of mathematical programming can be developed for and applied to computing optimal solutions for large instances of a classical geometric optimization problem with an uncountable number of constraints and variables.

The Art Gallery Problem (AGP) asks for placing a minimum number of stationary guards in a polygonal region $P$, such that all points in $P$ are guarded. The AGP is NP-hard, even to approximate. Due to the infinite number of points to be guarded as well as possible guard positions, applying mathematical programming methods for computing provably optimal solutions is far from straightforward.

In this paper, we use an iterative primal-dual relaxation approach for solving AGP instances to optimality. At each stage, a pair of LP relaxations for a finite candidate subset of primal covering and dual packing constraints and variables is considered; these correspond to possible guard positions and points that are to be guarded.

Of particular interest are additional cutting planes for eliminating fractional solutions. We identify two classes of facets, based on Edge Cover and Set Cover (SC) inequalities. Solving the separation problem for the latter is NP-complete, but exploiting the underlying geometric structure of the AGP, we show that large subclasses of fractional SC solutions cannot occur for the AGP. This allows us to separate the relevant subset of facets in polynomial time.

Finally, we characterize all facets for finite AGP relaxations with coefficients in ${0, 1, 2}$. We demonstrate the practical usefulness of our approach with improved solution quality and speed for a wide array of large benchmark instances.
URL for the Abstract:
http://arxiv.org/abs/1308.4670
Keywords:
Art Gallery Problem, geometric optimization, algorithm engineering, set cover polytope, solving NP-hard problem instances to optimality
Download
Access Level:
Internal

Correlation
MPG Unit:
Max-Planck-Institut für Informatik
MPG Subunit:
Algorithms and Complexity Group
External Affiliations:
TU Braunschweig
Audience:
experts only
Appearance:
MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort



BibTeX Entry:

@INPROCEEDINGS{ffks-ffagp-13,
AUTHOR = {Fekete, S{\'a}ndor P. and Friedrichs, Stephan and Kr{\"o}ller, Alexander and Schmidt, Christiane},
EDITOR = {Du, Ding-Zhu and Zhang, Guochuan},
TITLE = {Facets for Art Gallery Problems},
BOOKTITLE = {Computing and Combinatorics},
PUBLISHER = {Springer},
YEAR = {2013},
VOLUME = {7936},
PAGES = {208--220},
SERIES = {Lecture Notes in Computer Science},
ADDRESS = {Hangzhou, China},
MONTH = {June},
ISBN = {978-3-642-38767-8},
DOI = {10.1007/978-3-642-38768-5_20},
}


Entry last modified by Stephan Friedrichs, 10/08/2014
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Editor(s)
Stephan Friedrichs
Created
10/08/2014 02:30:34 PM
Revision
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Editor
Stephan Friedrichs
Stephan Friedrichs


Edit Date
10/08/2014 04:11:43 PM
10/08/2014 02:30:34 PM