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Conference Paper

#### Optimal Compaction of Orthogonal Grid Drawings

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##### Citation

Klau, G. W., & Mutzel, P. (1999). Optimal Compaction of Orthogonal Grid Drawings.
In G. Cornuéjols, R. E. Burkard, & G. J. Woeginger (*Proceedings
of the 7th International Conference on Integer Programming and Combinatorial Optimization (IPCO-99)* (pp. 304-319).
Berlin: Springer.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-35EE-7

##### 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.