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  Optimal Compaction of Orthogonal Grid Drawings

Klau, G. W., & Mutzel, P. (1999). Optimal Compaction of Orthogonal Grid Drawings. 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. 304-319). Berlin: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-35EE-7 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-35F0-0
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: We consider the two--dimensional compaction problem for orthogonal grid drawings in which the task is to alter the coordinates of the vertices and edge segments while preserving the shape of the drawing so that the total edge length is minimized. The problem is closely related to two--dimensional compaction in VLSI--design and has been shown to be NP--hard. We characterize the set of feasible solutions for the two--dimensional compaction problem in terms of paths in the so--called constraint graphs in $x$-- and $y$--direction. Similar graphs (known as \emph{layout graphs}) have already been used for one--dimensional compaction in VLSI--design, but this is the first time that a direct connection between these graphs is established. Given the pair of constraint graphs, the two--dimensional compaction task can be viewed as extending these graphs by new arcs so that certain conditions are satisfied and the total edge length is minimized. We can recognize those instances having only one such extension; for these cases we solve the compaction problem in polynomial time. We transform the geometrical problem into a graph--theoretical one and formulate it as an integer linear program. Our computational experiments show that the new approach works well in practice.

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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: 518027
Other: Local-ID: C1256428004B93B8-9FA8605E67ABCFDFC125680A005C782E-KlauMutzel1999a
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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: 304 - 319 Identifier: -

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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: ISSN: 0302-9743