The constrained crossing minimization problem: a first approach

Mutzel, Petra; Ziegler, Thomas

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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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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-3611-B Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-3612-9

Genre: Conference Paper

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Creators:
Mutzel, Petra¹, Author
Ziegler, Thomas¹, Author

Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019

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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.

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Language(s): eng - English

Dates: Modified: 2010-03-02Date issued: 1999

Publication Status: Issued

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Publishing info: Berlin : Springer

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Identifiers: eDoc: 517970
Other: Local-ID: C1256428004B93B8-1609739ACECAF0D3C1256714004FDF45-MutzelZiegler1998

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Title: Untitled Event

Place of Event: Zurich, Switzerland

Start-/End Date: 1999

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Title: Operations Research Proceedings 1998

Source Genre: Proceedings

Creator(s):
Kall, Peter, Editor
Lüthi, Hans-Jakob, Editor

Affiliations:
-

Publ. Info: Berlin : Springer

Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 125 - 134 Identifier: ISBN: 3-540-65381-3