Circuit placement on arbitrarily shaped regions using the self-organization principle

In this paper, we present an algorithm, called selforganization assisted placement (SOAP), for circuit placement in arbitrarily shaped regions, including two-dimensional rectilinear regions, nonplanar surfaces of three-dimensional objects, and three-dimensional volumes. SOAP is based on a learning algorithm for neural networks proposed by Kohonen [l], called self-organization, which adjusts the weight of synapses connected to neurons such that topologically close neurons become sensitive to inputs that are physically similar. In contrast to earlier methods on circuit placement in rectilinear region, where the final placement heavily depends on an arbitrary partition of the entire region into a number of rectangular subregions, thus leading to suboptimal results, SOAP is a general algorithm for circuit placement in arbitrarily shaped regions without these drawbacks. A standard cell placement method and a global placement method of macro cells using SOAP algorithm are also described. Several examples showing the circuit placement on rectilinear regions, nonplanar surfaces, and 3-D volumes are shown. Experimental results on benchmark circuits show that the SOAP algorithm is competitive with the state-of-the-art algorithms even for the case of placement in a rectangular region, which is a special case of a 2-D rectilinear region.