Minimum Separation for Single-Layer Channel Routing

We present a linear-time algorithm for determining the minimum height of a single-layer routing channel. The algorithm handles single-sided connections and multiterminal nets. It yields a simple routability test for single-layer switchboxes, correcting an error in the literature

Compact Channel-Routing of Multiterminal Nets

Coordinated Science Laboratory was formerly known as Control Systems LaboratorySemiconductor Research Corporation / 83-01-035National Science Foundation / MCS-81-0555

3-dimensional Channel Routing

Consider two parallel planar grids of size w × n . The vertices of these grids are called terminals and pairwise disjoint subsets of termi nals are called nets. We aim at routing all nets in a cubic grid between the two layers h olding the terminals. However, to ensure solvability, it is allowed to introduce a n empty row/column be- tween every two consecutive rows/columns containing the te rminals (in both grids). Hence the routing is to be realized in a cubic grid of size 2 n × 2 w × h . The objective is to minimize the height h . In this paper we generalize previous results of Recski and Szeszl ́er [10] and show that every problem instance is so lvable in polynomial time with height h = O (max( n, w )). This linear bound is best possible (apart from a constant factor)

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 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(lgN) time on a CREW PRAM or O(lgN / lglgN) 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(lgN lglgN) on a CREW PRAM or O(lgN / lglgN) time on a CRCW PRAM with O(N lglgN) 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. 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

On the Complexity of the General Channel Routing Problem in the Knock-Knee Mode

Coordinated Science Laboratory was formerly known as Control Systems LaboratorySemiconductor Research Corporation / 84-06-04