# The ICICS/CS Reading Room

## UBC CS TR-86-11 Summary

- No on-line copy of this technical report is available.

- Model \& Solution Strategy for Placement of Rectangular Blocks in the Euclidean Plane, May 1986 Amir Alon and Uri Ascher
This paper describes a nonlinear optimization model for the placement of
rectangular blocks with some wire connections among them in the Euclidian
plane, such that the total wire length is minimized. Such a placement
algorithm is useful as a CAD tool for VLSI and PCB layout designs.

The mathematical model presented here ensures that the blocks will not
overlap and minimizes the sum of the distances of the interconnections of
the blocks with respect to their orientation as well as their position. We
also present mechanisms for solving more restrictive placement problems,
including one in which there is a set of equally spaced, discrete angles to be
used in the placement. The mathematical model is based on the Lennard-Jones
6-12 potential equation, on a sine wave shaped penalty function, and
on minimizing the sum of the squares of the Euclidian distances of the block
interconnections. We also present some experimental results which show
that good placements are achieved with our techniques.

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