1. 1 NTUplace: A Partitioning Based Placement Algorithm for Large-Scale Designs Tung-Chieh Chen 1, Tien-Chang Hsu 1, Zhe-Wei Jiang 1, and Yao-Wen Chang 1,2 Graduate Institute of Electronics Engineering 1 Department of Electrical Engineering 2 National Taiwan University Taipei, Taiwan April 6, 2005

2. 2 National Taiwan University Outline ․ Introduction ․ Global placement  HPWL modeling with min-cut  Whitespace management  Look-ahead partitioning ․ Legalization ․ Detailed placement  Matching based detailed placement ․ Results

3. 3 National Taiwan University Introduction ․ NTUplace is based on the min-cut partitioning technique. ․ Algorithm: Global Placement Legalization Detailed Placement Wirelength modeling with min-cut Whitespace management Look-ahead partitioning Matching based detailed placement

4. 4 National Taiwan University HPWL Modeling with Min-Cut ․ The HPWL (half-perimeter wirelength) is exactly modeled with the min-cut objective.  Finding the min-cut is equivalent to finding the minimum HPWL. ․ The idea is similar to the Bounding Box aware Terminal Propagation (BBTP) in the TheTo placer:  Selvakkumaran and Karypis, Technical Report 04-040, Univ. of Minnesota. Oct. 2004. ․ They use 7 cases to discuss the HPWL modeling. ․ We derive a unified method for the modeling. ․ Our method can be applied to the diagonal-bin repartitioning.  TheTo might need to consider tens of cases.

5. 5 National Taiwan University Net-Weight Assignment (1/2) ․ For each net, we compute three HPWL values. ․ Consider the case for a net with 2 fixed pins and 2 movable cells, and the x-range of the 2 pins is within that of the 2 cells and the center of the left partition is closer to the x-range  w 1 : the wirelength when the 2 cells are at the left side  w 2 : the wirelength when the 2 cells are at the right side,  w 12 : the wirelength when the 2 cells are at different sides.  Here, w 12 > w 2 > w 1 2 cells are at the left side. 2 cells are at the right side. 2 cells are at different side. Fixed pin Movable cell HPWL = w 1 HPWL = w 2 HPWL = w 12 (Fixed pin) X-range

6. 6 National Taiwan University Net-Weight Assignment (2/2) ․ Introduce a partitioning graph (hypergraph) and two fixed nodes to represent the two sides. ․ Add two hyperedges into the graph.  Since w 2 > w 1, assign the weight of the hyperedge e 1 between the cells and the left fixed node be (w 2 -w 1 ).  Assign the weight of the hyperedge e 2 between the two cells be (w 12 -w 2 ). ․ Partition the resulting hypergraph to decide the cell/node partition. weight(e 1 ) = (w 2 -w 1 ) weight(e 2 ) = (w 12 -w 2 ) Left fixed node Right fixed node Movable node

7. 7 National Taiwan University Three Possible Partitioning Results Movable node Fixed node e1e1 e2e2 e2e2 e1e1 e1e1 e2e2 weight(e 1 ) = (w 2 -w 1 ) weight(e 2 ) = (w 12 -w 2 ) Left fixed nodeRight fixed node Movable node 2 1 3

8. 8 National Taiwan University Relationship Between HPWL and Cutsize n cut = 0 n cut = weight(e 1 ) = (w 2 -w 1 ) n cut = weight(e 1 )+ weight(e 2 ) = (w 12 -w 2 ) + (w 2 -w 1 ) = (w 12 -w 1 ) HPWL = w 1 = w 1 + n cut HPWL = w 2 = w 1 + n cut HPWL = w 12 = w 1 + n cut e1e1 e2e2 e2e2 e1e1 e1e1 e2e2 All three cases: HPWL = w 1 + n cut 123

9. 9 National Taiwan University ․ Theorem: HPWL = w 1 + n cut. ․ Then, we have Finding the minimum HPWL is equivalent to finding the min-cut. Relationship Between HPWL and Cutsize (Constant)

10. 10 National Taiwan University Whitespace Management (1/2) ․ Traditional min-cut placers uniformly distribute whitespace and tend to produce excessive wirelength when the whitespace is large. ․ Adya, Markov, Villarrubia use filler (dummy) cells to control the whitespace allocation [ICCAD-03].  Add dummy cells to increase the utilization. Whitespace is distributed according to the dummy cell locations.  However, their method tend to increase the number of cells, leading to longer running time and larger memory usage.

11. 11 National Taiwan University ․ We directly control the balance criteria during partitioning using the available free space. ․ Relaxing the balance criteria leads to smaller cutsize and thus smaller wirelength. ․ The balance criterion satisfies that the utilization of each partition is less than or equal to 1. ․ The criterion is fed into the partitioner to allocate whitespace. Whitespace Management (2/2) Both util. < 1 Block Area Left util. = 1, right util. < 1 Block Area Left util. < 1, right util. = 1 Uniform whitespace distribution Left partition Utilization = 1.0 Right partition Utilization = 1.0

12. 12 National Taiwan University Look-Ahead Partitioning ․ Simplify the idea in Cong et al., “ Fast floorplanning by look-ahead enabled recursive bipartitioning, ” ASPDAC- 2005. ․ Use the first-fit bin-packing heuristic to check if the subpartition can be legalized.  Increase the chance of legalizing macro blocks. ․ If the subpartition cannot be legalized, we move the cutline and redo the partitioning. Legalization Fails Re- partition Legalization Succeeds

13. 13 National Taiwan University 41 Legalization ․ Place all cells in the rows to obtain a feasible solution. 1)Place cells into their nearest rows. 2)Sort all standard cells according to their sizes, from the largest to the smallest. 3)Assign the x-coordinates for all cells according to the sorted order. If overlap occurs, we will find a nearest empty slot to place the cell. 23 5 Place cells into nearest rows 23 145 Sort the cells Place cells one-by-one

14. 14 National Taiwan University ․ Is based on cell location assignment (matching).  Each cell has different costs at different locations.  Minimize total cost: O(n 3 ) time for n cells  Is better than O(n!) time for a branch & bound (BB) detailed placer  Can use a much larger window (> 64 cells) Detailed Placement ABC 123

15. 15 National Taiwan University Old Results ․ Old results in the ISPD-05 proceedings. CircuitObjectsNetsFinal HPWL (um) Global Placement Runtime Total Runtime* adaptec1211,447221,1429.305 e74 min11 min adaptec3451,650466,7582.731 e815 min28 min *On a Pentium 4 3.2GHz PC

16. 16 National Taiwan University New Results from the Enhanced Methods ․ Enhance our placer with matching based detailed placement and other schemes (e.g., repartitioning). ․ Improve the published HPWL by 10%. CircuitPublished HPWL Final HPWL Published Runtime Final Runtime adaptec19.305 e78.472 e711 min50 min adaptec32.731 e82.436 e828 min160 min Comp.1.000.901.005.13

17. 17 National Taiwan University Thank you for your attention!