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  The constrained crossing minimization problem: a first approach

Mutzel, P., & Ziegler, T. (1999). The constrained crossing minimization problem: a first approach. In P. Kall, & H.-J. Lüthi (Eds.), Operations Research Proceedings 1998 (pp. 125-134). Berlin: Springer.

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 Urheber:
Mutzel, Petra1, Autor           
Ziegler, Thomas1, Autor           
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Zusammenfassung: 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.

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Sprache(n): eng - English
 Datum: 2010-03-021999
 Publikationsstatus: Erschienen
 Seiten: -
 Ort, Verlag, Ausgabe: Berlin : Springer
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: eDoc: 517970
Anderer: Local-ID: C1256428004B93B8-1609739ACECAF0D3C1256714004FDF45-MutzelZiegler1998
 Art des Abschluß: -

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Titel: Untitled Event
Veranstaltungsort: Zurich, Switzerland
Start-/Enddatum: 1999

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Titel: Operations Research Proceedings 1998
Genre der Quelle: Konferenzband
 Urheber:
Kall, Peter, Herausgeber
Lüthi, Hans-Jakob, Herausgeber
Affiliations:
-
Ort, Verlag, Ausgabe: Berlin : Springer
Seiten: - Band / Heft: - Artikelnummer: - Start- / Endseite: 125 - 134 Identifikator: ISBN: 3-540-65381-3