ece 6133 project overviewlimsk.ece.gatech.edu/course/ece6133/6133-project-intro-2021.pdf · ece...
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ECE 6133 Project OverviewSpring 2021
Sung Kyu [email protected] Institute of Technology
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• Circuit partitioning using matrices and eigenvectors
1/4. EIG Partitioning
Laplacian matrix L
2nd smallest eigenvector of Lgives linear placement
3
• IBM18 benchmark– 210,613 cells
– Laplacian matrix fill rate: 0.01%!
– 178 GB of memory required to store in a normal matrix
– Sparse matrix can bring that down to 2.5 MB
Laplacian Sparsity
4Cutsize vs. Ratio Cut Landscape
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• Use linear equations to formulate floorplaning
2/4. ILP Floorplanning
…..
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• Off-the-shelf solver gives:
Obtaining ILP Solutions
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• Can size soft modules– Linear approximation used: overlap (or whitespace) may occur
Handling Hard/Soft Modules
floorplan with overlapred: soft, yellow: rotated using “super blocks”
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• Steiner points– Reduce the overall wirelength– Finding Steiner points is NP-hard….– So, we rely on heuristics
Recti-linear Routing with Steiner Points
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• Strategy: build separable MST and improve with L-edges
3/4. L-Shaped Steiner Routing
upper upper
lower lower upper
lower lower/upper upper
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• Strategy: build MST and add single Steiner point at a time
3/4. Kahng/Robins Routing
11Sample Routing Result
initial MST(WL = 242)
final RST (WL = 218)22 Steiner points added
Took 3 min
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• Cost minimization problem– How do we ship the units so that the overall cost is minimized?– Assume the capacity of each edge is 5 units
Multi-Commodity Flow (MCF) Problem
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• Set up ILP for MCF routing– Capacity of each edge in G is 2– Each edge in G becomes a pair of bi-directional arcs in F– n1 = {a,l}, n2 = {i,c}, n3 = {d,f}, n4 = {k,d}, n5 = {g,h}, n6 = {b,k}
MCF-based Multi-net Routing
14ILP Formulation
objective function
demand constraints
capacity constraints
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• Using off-the-shelf ILP solver
ILP-based Routing Solution
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• Based on shortest paths and rip-up-and-reroute
Heuristic: MM Algorithm
17Sample Routing Results
350 net benchmarkusage 1:1849 edgesusage 2:2468 edges
200 net benchmarkusage 1:1298 edgesusage 2: 1412 edges
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• Congestion maps– Thickness and color intensity indicate routing congestion
Sample Routing Results (cont)
30 nets 80 nets 200 nets