Parallel Algorithms for Single-Layer Channel Routing

Abstract

We provide efficient parallel algorithms for the minimum separation, offset range, and optimal offset problems for single-layer channel routing. We consider all the variations of these problems that are known to have linear-time sequential solutions rather than limiting attention to the "river-routing" context, where single-sided connections are disallowed. For the minimum separation problem, we obtain O( lg N) time on a CREW PRAM or [Formula: see text] time on a (common) CRCW PRAM, both with optimal work (processor-time product) of O(N), where $N$ is the number of terminals. For the offset range problem, we obtain the same time and processor bounds as long as only one side of the channel contains single-sided nets. For the optimal offset problem with single-sided nets on one side of the channel, we obtain time O( lg N lg lg N) on a CREW PRAM or [Formula: see text] time on a CRCW PRAM with O(N lg lg N) work. Not only does this improve on previous results for river routing, but we can obtain an even better time of O(( lg lg N)2) on the CRCW PRAM in the river routing context. In addition, wherever our results allow a channel boundary to contain single-sided nets, the results also apply when that boundary is ragged and N incorporates the number of bendpoints.