Optimal Placement for River Routing

River routing is the problem of connecting a set of terminals a₁,…,a_n on a line to another set b₁,…,b_n in order across a rectangular channel. When 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. This paper gives concise necessary and sufficient conditions for wirability which are applied to reduce the optimal placement problem to the graph-theoretic single-source-longest-paths problem. 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.