Manhattan-diagonal routing in channels and switchboxes

Abstract

New techniques are presented for routing straight channels, L-channels, switchboxes, and staircase channels in a two-layer Manhattan-diagonal (MD) model with tracks in horizontal, vertical, and ± 45° directions. First, an O ( l.d ) time algorithm is presented for routing a straight channel of length l and density d with no cyclic vertical constraints . It is shown that the number of tracks h used by the algorithm for routing multiterminal nets satisfies d ≤ h ≤ ( d + 1). Second, an output-sensitive algorithm is reported that can route a channel with cyclic vertical constraints in O ( l.h ) time using h tracks, allowing overlapping of wire segments in two layers. Next, the routing problem for a multiterminal L-channel of length l and height h is solved by an O ( l.h ) time algorithm. If no cyclic vertical constraints exist, its time complexity reduces to O ( l.d ) where d is the density of the L-channel. Finally, the switchbox routing problem in the MD model is solved elegantly. These techniques, easily extendible to the routing of staircase channels, yield efficient solutions to detailed routing in general floorplans. Experimental results on benchmarks show significantly low via count and reduced wire length, thus establishing the superiority of MD routing to classical strategies. The proposed algorithms are also potentially useful for general non-Manhattan area routing and multichip modules (MCMs).