Parallel Algorithms for Single-Layer Channel Routing

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 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(lgN) time on a CREW PRAM or O(lgN/lglgN) time on a 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 $O(lgNlglgN)$ on a CREW PRAM or O(lgN) time on a CRCW PRAM with O(NlglgN) work. Not only does this improve on previous results for river routing, but we can obtain an even better time of O((lglgN)^{2}) on the CRCW PRAM in the river routing context.