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Special-purpose hardware has been proposed as a solution to several increasingly complex problems in design automation. This paper examines a class of cellular architectures called raster pipeline subarrays--RPS architectures--applicable to problems in physical DA that are (1) representable on a cellular grid, and (2) characterized by local functional dependencies among grid cells. Machines with this architecture first evolved in conventional cellular applications that exhibit similarities to grid-based DA problems. To analyze the properties of the RPS organization in context, machines designed for cellular applications are reviewed, and it is shown that many DA machines proposed/constructed for grid-based problems fit naturally into a taxonomy of cellular machines. The implementation of DA algorithms on RPS hardware is partitioned into local issues that involve the processing of individual cell neighborhoods, and global issues that involve strategies for handling complete grids in a pipeline environment. Design rule checking and routing algorithms are examined in an RPS environment with respect to these issues. Experimental measurements for such algorithms running on an existing RPS machine exhibit significant speedups. From these studies are derived the necessary performance characteristics of RPS hardware optimized specifically for grid-based DA. Finally, the practical merits of such an architecture are evaluated.