Nearly optimal algorithms and bounds for multilayer channel routing

Abstract

This paper presents algorithms for routing channels with L ≥2 layers. For the unit vertical overlap model, we describe a two-layer channel routing algorithm that uses at most d + O(√d) tracks to route two-terminal net problems and 2d + O(√d) tracks to route multiterminal nets. We also show that d + Ω(log d) tracks are required to route two-terminal net problems in the worst case even if arbitrary vertical overlap is allowed. We generalize the algorithm to unrestricted multilayer routing and use only d/(L -1) + O(√d/L + 1)> tracks for two-terminal net problems (within O(√d/L + 1) tracks of optimal) and d/(L-2) +O(√d/L + 1) tracks for multiterminal net problems (within a factor of(L-1)/(L-2) times optimal). We demonstrate the generality of our routing strategy by showing that it can be used to duplicate some of the best previous upper bounds for other models (two-layer Manhattan routing and two and three-layer knock-knee routing of two-terminal, two-sided nets), and gives a new upper bound for rotuing with 45-degree diagonal wires.