Buffered Steiner Trees for Difficult Instances

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Presentation transcript:

Buffered Steiner Trees for Difficult Instances Charles J. Alpert, Gopal Gandham, Milos Hrkic, John Lillis, Jiang Hu, Andrew B. Kahng, Bao Liu, Stephen T. Quay, Sachin S. Sapatnekar, Andrew J. Sullivan

Min-Cost Steiner Tree Late 1980s

Timing-driven Steiner Tree Early 1990s

Buffered Steiner Tree Mid 1990s

Blockage Aware Trees Present

Ripping out Synthesis Trees Ugly pre-PD buffered trees Inverted sinks Trivial van Ginneken/Lillis change Normal sinks: one positive candidate Inverted sinks: one negative candidate No big deal

Or Is It? _ +

But Look What Happens _ +

Buffer Aware Trees

The Texas Two Step Optimal Unrouted net with placed pins Construct Buffered Steiner Tree Construct Steiner Tree Dynamic Programming Buffer Insertion Simultaneous Tree Construction And Buffer Insertion Optimal

C-Tree Algorithm A-, B-, H-, O-, P-, trees taken Cluster sinks by Polarity Manhattan distance Criticality Two-level tree Form tree for each cluster Form top-level tree

C-Tree Example

Net n8702 (44 sinks) C-Tree (9) 258 11 4386 0.9 C-Tree (2) 355 9 7688 Algorithm Worst slack buffers wire CPU Time C-Tree (9) 258 11 4386 0.9 C-Tree (2) 355 9 7688 1.5 Flat C-Tree -101 26 4061 1.4 P-Tree 99 19 4089 4.1 BP-Tree 295 21 4119 861

Net n8702

Flat C-Tree

C-Tree 4 clusters

C-Tree 2 clusters

Difficult Steiner Instances Polarity/size makes it hard 3d trade-off Timing Buffers Wire length Work on it!