The complexity of single row routing

This paper investigates a systematic suboptimal approach to multilayer rectilinear wire routing: the single row approach. The method involves decomposing the general rectilinear wiring problem into a number of conceptually simpler single row problems. The complexity of the decomposition process is first considered. Under interesting optimization criteria, each step in the decomposition process is shown to be NP-hard. Then the single row wiring problem itself is considered under a variety of optimization criteria. In some cases, either efficient or "usually good" algorithms are possible. In other cases, the problem turns out to be NP-hard.