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#### Optimal compaction of orthogonal grid drawings

##### MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44788

Klau,  Gunnar W.
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45092

Mutzel,  Petra
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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##### Fulltext (public)

1998-1-031
(Any fulltext), 11KB

##### Supplementary Material (public)
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##### Citation

Klau, G. W., & Mutzel, P.(1998). Optimal compaction of orthogonal grid drawings (MPI-I-1998-1-031). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-7B5A-6
##### 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 {\sc VLSI}--design and is conjectured to be {\sl 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 {\em layout graphs}) have already been used for one--dimensional compaction in {\sc 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 can solve the compaction problem in polynomial time. We have transformed the geometrical problem into a graph--theoretical one which can be formulated as an integer linear program. Our computational experiments have shown that the new approach works well in practice. It is the first time that the two--dimensional compaction problem is formulated as an integer linear program.