1. Joanna Ellis-Monaghan, St. Michaels College Paul Gutwin, Principal Technical Account Manager, Cadence.

2. Netlist Layout, Boca Raton '032 A set S of nodes ( the pins) hundreds of thousands. A partition P 1 of the pins (the gates) 2 to 1000 pins per gate, average of about 3.5. A partition P 2 of the pins (the wires) again 2 to 1000 pins per wire, average of about 3.5. A maximum permitted delay between each pair of pins (infinite unless there is a wire between the pins). Netlist

3. Netlist Layout, Boca Raton '033 Example Gate Pin Wire

4. Netlist Layout, Boca Raton '034 The Wires

5. Netlist Layout, Boca Raton '035 The Wiring Space Placement layer- gates/pins go here Vias (vertical connectors) Horizontal wiring layer Vertical wiring layer Up to 12 or so layers

6. Netlist Layout, Boca Raton '036 Netlist Layout Place the pins so that pins are in their gates on the placement layer with non-overlapping gates. Place the wires in the wiring space so that the delay constrains on pairs of pins are met, where delay is proportional to minimum distance within the wiring, and via delay is negligible

7. Netlist Layout, Boca Raton '037 Placement

8. Netlist Layout, Boca Raton '038 A Few Basic Questions Partition the netlist Leverage the hierarchy Identify congestion Automate small configurations

9. Netlist Layout, Boca Raton '039 Partitioning Divide the pins/gates into k roughly equal parts, minimizing the number of hyperedges in the cutset. Optimal hypergraph bisection is NP Approximation heuristics—e.g. ‘coarsen’ the hypergraph by merging vertices, bisect, then ‘uncoarsen’ and refine. (See Karypis, Aggarwal, Kumar, Shekhar: Multilevel Hypergraph Partitioning: Application in VLSI Domain)

10. Netlist Layout, Boca Raton '0310 Leverage the Hierarchy Designers think in ‘modules’ Use the hierarchy tree to inform the partitioning. * * * * * * * * * * (Netlist Level) * * * * * * *

11. Netlist Layout, Boca Raton '0311 Identify Congestion Identify dense substructures from the netlist Develop a congestion ‘metric’ Brambles and tree width may be appropriate tools for this. A B C D F G EH Congested area Routing

12. Netlist Layout, Boca Raton '0312 Congested area What often happens What would be good Real Life Congestion Examples

13. Netlist Layout, Boca Raton '0313 Automate Wiring Small Configurations Some are easy to place and route Simple left to right logic No / few loops (circuits) Uniform, low fan-out Statistical models work Some are very difficult E.g. ‘Crossbar Switches’ Many loops (circuits) Non-uniform fan-out Statistical models don’t work

14. Netlist Layout, Boca Raton '0314 Control Signals Crossbar Switch

15. Netlist Layout, Boca Raton '0315 Control Signals Single Direction Crossbar Switch

16. Netlist Layout, Boca Raton '0316 Control Signals Substructure (Minimal layouts established for very regular structures: Mathukrishanan, Paterson, Sahinalp, Suel: Compact Grid Layouts of Multi-Level Networks, but no general heuristic)

17. Netlist Layout, Boca Raton '0317 Some Possible Models (Di)graph: pins = vertices, edges between pins which are connected. Graph: gates = vertices, edges between gates which are connected. Two Hypergraphs: pins = vertices, H 1 =pins on the same gates, H 2 = connected pins. (each vertex is in exactly one hyperedge in each of H 1 and H 2,, and a hyperedge in H 1 intersects a hyperedge in H 2 in at most one vertex) Single Hypergraph: gates = vertices, H = connected gates (ie contract H 1 in the model above).

18. Netlist Layout, Boca Raton '0318 Some Potential Tools Grid graphs Geometric thickness Graph drawing algorithms Hypergraph embeddings Need to translate results to the wiring space!!