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  Combining Graph Labeling and Compaction

Klau, G. W., & Mutzel, P. (1999). Combining Graph Labeling and Compaction. In J. Kratochvíl (Ed.), Proceedings of the 7th International Symposium on Graph Drawing (GD-99) (pp. 27-37). Berlin: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-35B1-D Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-35B3-9
Genre: Conference Paper

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 Creators:
Klau, Gunnar W.1, Author           
Mutzel, Petra1, Author           
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: Combinations of graph drawing and map labeling problems yield challenging mathematical problems and have direct applications, \emph{e.g.}, in automation engineering. We call graph drawing problems in which subsets of vertices and edges need to be labeled \emph{graph labeling problems}. Unlike in map labeling where the position of the objects is specified in the input, the coordinates of vertices and edges in a graph drawing problem instance are yet to be determined and thus create additional degrees of freedom. We concentrate on the \emph{Compaction and Labeling (COLA) Problem}: Given an orthogonal representation---as produced by algorithms within the topology--shape--metrics paradigm---and some label information, the task is to generate a labeled orthogonal embedding with minimum weighted sum of edge length and perimeter. We characterize feasible solutions of the \emph{COLA} problem extending an existing framework for solving pure compaction problems. Based on the graph--theoretical characterization, we present a branch--and--cut algorithm which computes optimally labeled orthogonal drawings for given instances of the \emph{COLA} problem. Computational experiments on a benchmark set of practical instances show that our method is superior to the traditional approach of applying map labeling algorithms to graph drawings. To our knowledge, this is the first algorithm especially designed to solve graph labeling problems.

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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: 518052
Other: Local-ID: C1256428004B93B8-BEAECCF6C5B8CA77C12568A900362FDF-KlauMutzel1999
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Title: Untitled Event
Place of Event: Stirin Castle, Czech Republic
Start-/End Date: 1999

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Title: Proceedings of the 7th International Symposium on Graph Drawing (GD-99)
Source Genre: Proceedings
 Creator(s):
Kratochvíl, Jan, Editor
Affiliations:
-
Publ. Info: Berlin : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 27 - 37 Identifier: -

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Publ. Info: -
Pages: - Volume / Issue: 1731 Sequence Number: - Start / End Page: - Identifier: ISSN: 0302-9743