Optimal Placement for River Routing

Abstract

Programs for integrated circuit layout typically have two phases: placement and routing. The router should produce as efficient a layout as possible, but of course the quality of the routhing depends heavily on the quality of the placement. On the other hand, the placement procedure ideally should know the quality of a routing before it routes the wires. In this talk we present an optimal solution for a practical, common version of this placement and routing problem. River routing is the problem of connecting in order a set of terminals a1,...,an on a line to another set b1,...,bn across a rectangular channel. Since the terminals are located on modules, the modules must be placed relative to one another before routing. This placement problem arises frequently in design systems like bristle-blocks where stretch lines through a module can effectively break it into several chunks, each of which must be placed separately. In this talk, we shall present concise necessary and sufficient conditions for wirability which are applied to reduce the optimal placement problem to the graph-theoretic single-source-longest-paths problems. By exploiting the special structure of graphs that arise from the placement problem for rectilinear wiring, an optimal solution may be determined in linear time.