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 Proceedings Article, Paper @InProceedings Beitrag in Tagungsband, Workshop
 Author, Editor
 Author(s): Mutzel, Petra Ziegler, Thomas dblp dblp
 Editor(s): Kall, Peter Lüthi, Hans-Jakob dblp dblp
 BibTeX cite key*: MutzelZiegler1998
 Title, Booktitle
 Title*: The constrained crossing minimization problem: a first approach Booktitle*: Operations Research Proceedings 1998
 Event, URLs
 Conference URL:: Downloading URL: Event Address*: Zurich, Switzerland Language: English Event Date* (no longer used): August 31 - September 3, 1998 Organization: Event Start Date: 24 November 2020 Event End Date: 24 November 2020
 Publisher
 Name*: Springer URL: Address*: Berlin Type:
 Vol, No, Year, pp.
 Series:
 Volume: Number: Month: Pages: 125-134 Year*: 1999 VG Wort Pages: ISBN/ISSN: 3-540-65381-3 Sequence Number: DOI:
 (LaTeX) Abstract: We investigate the {\em constrained crossing minimization problem} for graphs defined as follows. Given a connected, planar graph $G=(V,E)$, a combinatorial embedding $\Pi(G)$ of $G$, and a set of pairwise distinct edges $F\subseteq V\times V$, find a drawing of $G\cup F$ in the plane such that the combinatorial embedding $\Pi(G)$ of $G$ is preserved and the number of edge crossings is minimum. This problem arises in the context of automatic graph drawing. Here, the so--called planarization method transforms a general graph into a planar graph and then applies planar graph drawing methods to it. First we show NP--hardness of this problem. Then we formulate an $|F|$--pairs shortest walks problem on an extended dual graph, where the number of crossings between the walks is added to the cost function. We show that this dual problem is equivalent to our original problem. Our approach to solve the dual problem is based on polyhedral combinatorics. We investigate an ILP--formulation and present first computational results using a branch--and--cut algorithm based on ABACUS. Keywords: Crossing Minimization, Graph Drawing, Integer Linear Programming Download Access Level:

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BibTeX Entry:

@INPROCEEDINGS{MutzelZiegler1998,
AUTHOR = {Mutzel, Petra and Ziegler, Thomas},
EDITOR = {Kall, Peter and L{\"u}thi, Hans-Jakob},
TITLE = {The constrained crossing minimization problem: a first approach},
BOOKTITLE = {Operations Research Proceedings 1998},
PUBLISHER = {Springer},
YEAR = {1999},
PAGES = {125--134},
ADDRESS = {Zurich, Switzerland},
ISBN = {3-540-65381-3},
}

Entry last modified by Anja Becker, 03/02/2010
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 Editor(s) Thomas Ziegler Created 02/10/1999 03:32:25 PM Revisions 4. 3. 2. 1. 0. Editor(s) Anja Becker Anja Becker Anja Becker Anja Becker Anja Becker Edit Dates 07.04.2000 10:02:40 30.03.2000 16:35:52 30.03.2000 16:34:47 30.03.2000 16:33:52 10/02/99 15:32:25