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  Optimizing Over All Combinatorial Embeddings of a Planar Graph

Mutzel, P., & Weiskircher, R. (1999). Optimizing Over All Combinatorial Embeddings of a Planar Graph. In G. Cornuéjols, R. E. Burkard, & G. J. Woeginger (Eds.), Proceedings of the 7th International Conference on Integer Programming and Combinatorial Optimization (IPCO-99) (pp. 361-376). Berlin: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-35F1-E Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-35F3-A
Genre: Conference Paper

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 Creators:
Mutzel, Petra1, Author           
Weiskircher, René1, Author           
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: We study the problem of optimizing over the set of all combinatorial embeddings of a given planar graph. Our objective function prefers certain cycles of $G$ as face cycles in the embed ding. The motivation for studying this problem arises in graph drawing, where the chos en embedding has an important influence on the aesthetics of the drawing. We characterize the set of all possible embeddings of a given biconnected planar graph $G$ by means of a system of linear inequalities with $\{0,1\}$-variables corresponding to the set of those cycles in $G$ which can appear in a combinator ial embedding. This system of linear inequalities can be constructed recursively using SPQR-trees and a new splitting operation. Our computational results on two benchmark sets of graphs are surprising: The nu mber of variables and constraints seems to grow only linearly with the size of the graphs although the number of embeddings grows exponentially. For all tested graphs (up to 500 vertices) and l inear objective functions, the resulting integer linear programs could be generated within 10 mi nutes and solved within two seconds on a Sun Enterprise 10000 using CPLEX.

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Language(s): eng - English
 Dates: 2010-03-021999
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 518024
Other: Local-ID: C1256428004B93B8-A772937AFE6EAE90C12567B6002E845F-Weiskircher1999
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Title: Untitled Event
Place of Event: Graz, Austria
Start-/End Date: 1999

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Title: Proceedings of the 7th International Conference on Integer Programming and Combinatorial Optimization (IPCO-99)
Source Genre: Proceedings
 Creator(s):
Cornuéjols, Gérard, Editor
Burkard, Rainer E., Editor
Woeginger, Gerhard J., Editor
Affiliations:
-
Publ. Info: Berlin : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 361 - 376 Identifier: ISBN: 3-540-66019-4

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Publ. Info: -
Pages: - Volume / Issue: 1610 Sequence Number: - Start / End Page: - Identifier: -