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Author, Editor
Author(s):
Mutzel, Petra
Weiskircher, René
dblp
dblp
Editor(s):
Chwa, Kyung-Yong
Ibarra, Oscar H.
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BibTeX cite key*:
Weiskircher1998
Title, Booktitle
Title*:
Two-Layer Planarization in Graph Drawing
Booktitle*:
Proceedings of the 9th International Symposium on Algorithms and Computation (ISAAC-98)
Event, URLs
URL of the conference:
http://jupiter.kaist.ac.kr/%7eisaac98/
URL for downloading the paper:
Event Address*:
Taejon, Korea
Language:
English
Event Date*
(no longer used):
December, 14-16
Organization:
Korea Information Science Society; Korea Advanced Institute of Science and Technology
Event Start Date:
19 September 2019
Event End Date:
19 September 2019
Publisher
Name*:
Springer
URL:
Address*:
Berlin, Germany
Type:
Vol, No, Year, pp.
Series:
Lecture Notes in Computer Science
Volume:
1533
Number:
Month:
December
Pages:
69-78
Year*:
1998
VG Wort Pages:
ISBN/ISSN:
3-540-65385-6
Sequence Number:
DOI:
Note, Abstract, ©
(LaTeX) Abstract:
We study the \tlpp s that have applications in Automatic Graph Drawing.
We are searching for a two-layer planar subgraph of maximum weight in a
given two-layer graph. Depending on the number of layers in which the vertices
can be permuted freely, that is, zero, one or two, different versions of the
problems arise. The latter problem was already investigated in \cite{Mut97}
using polyhedral combinatorics. Here, we study the remaining two cases and the
relationships between the associated polytopes.
In particular, we investigate the polytope $\calp _1$ associated with the
two-layer {\em
planarization} problem with one fixed layer. We provide an overview on the
relationships between
$\calp _1$ and the polytope $\calq _1$ associated with the two-layer {\em
crossing minimization}
problem with one fixed layer, the linear ordering polytope, the \tlpp\ with
zero and two layers
fixed. We will see that all facet-defining inequalities in $\calq _1$ are also
facet-defining for
$\calp _1$. Furthermore, we give some new classes of facet-defining
inequalities and show how the
separation problems can be solved. First computational results are presented
using a branch-and-cut
algorithm. For the case when both layers are fixed, the \tlpp\ can be solved in
polynomial time by a
transformation to the heaviest increasing subsequence problem. Moreover, we
give a complete
description of the associated polytope $\calp _2$, which is useful in our
branch-and-cut algorithm
for the one-layer fixed case.
Keywords:
Graph Drawing, Integer Optimization, Integer Linear Programming
HyperLinks / References / URLs:
http://www.mpi-sb.mpg.de/~weiski
Download
Access Level:
Correlation
MPG Unit:
Max-Planck-Institut für Informatik
MPG Subunit:
Algorithms and Complexity Group
Audience:
experts only
Appearance:
MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat
BibTeX Entry:
@INPROCEEDINGS
{
Weiskircher1998
,
AUTHOR = {Mutzel, Petra and Weiskircher, Ren{\'e}},
EDITOR = {Chwa, Kyung-Yong and Ibarra, Oscar H.},
TITLE = {Two-Layer Planarization in Graph Drawing},
BOOKTITLE = {Proceedings of the 9th International Symposium on Algorithms and Computation (ISAAC-98)},
PUBLISHER = {Springer},
YEAR = {1998},
ORGANIZATION = {Korea Information Science Society; Korea Advanced Institute of Science and Technology},
VOLUME = {1533},
PAGES = {69--78},
SERIES = {Lecture Notes in Computer Science},
ADDRESS = {Taejon, Korea},
MONTH = {December},
ISBN = {3-540-65385-6},
}
Entry last modified by Evelyn Haak, 03/02/2010
Edit History (please click the blue arrow to see the details)
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Editor(s)
René Weiskircher
Created
01/21/1999 02:06:01 PM
Revisions
5.
4.
3.
2.
1.
Editor(s)
Evelyn Haak
Uwe Brahm
Christine Kiesel
René Weiskircher
René Weiskircher
Edit Dates
01/04/99 13:10:43
29.03.99 18:33:43
25.03.99 16:30:30
09/02/99 21:54:58
05/02/99 15:10:23