Buffering in the Layout Environment - Computer Engineering ...

4.1 Tree Adjustment TechniqueAs a relatively easy method, one can start with a Steiner tree regardless blockages and modify thetree to avoid blockages [5]. This can be performed in a fashion similar to the rip-up-and-reroute incongestion avoidance of global routing. In other words, if a path in the tree has large overlap withblockages, it is ripped up and reconnected back to the tree with a path having less overlap withblockages. This is illustrated in Figure 28.7.aaascsdsdbbb(a) (b) (c)Figure 28.7: Rip-up-and-reroute to avoid blockages.In each iteration, the path with the largest overlap with blockages is chosen for rerouting.The reconnection procedure is done by running Dijkstra’s algorithm on the extended Hanan gridgraph indicated by the dashed lines in Figure 28.7. In this graph, the weight of an edge is itslength if it does not overlap with any blockage. If an edge overlaps with a blockage, its weightis its length times α, where α > 1 is a penalty coefficient. The value of α decides the tradeoffbetween blockage avoidance and wire increase due to detour. After the tree modification, thechance of feasible buffering solutions is increased. Since the rerouting has no knowledge if buffersare needed on a path, it may cause some unnecessary wire detours.Another technique is to integrate the tree adjustment with buffer insertion [6] so that wiredetour is incurred only when it is necessary for buffer insertion. The classic van Ginneken’s bufferinsertion algorithm [7] propagates a set of candidate solutions from the sink nodes toward thesource and picks the optimal one at the source. The adaptive tree adjustment technique generates acandidate solution with an alternative Steiner node if the original Steiner node is inside a blockage.This adjustment is a part of a candidate solution which is propagated toward the source. This8