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 Proceedings Article, Paper @InProceedings Beitrag in Tagungsband, Workshop
 Author, Editor
 Author(s): Mutzel, Petra Weiskircher, René dblp dblp
 Editor(s): Chwa, Kyung-Yong Ibarra, Oscar H. dblp dblp
 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
 Conference URL:: http://jupiter.kaist.ac.kr/%7eisaac98/ Downloading URL: 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: 7 July 2022 Event End Date: 7 July 2022
 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:
 (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:

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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},