Interconnect Implications of Growth-Based Structural Models for VLSI Circuits* Chung-Kuan Cheng, Andrew B. Kahng and Bao Liu UC San Diego CSE Dept. e-mail: {kuan,abk,bliu}@cs.ucsd.edu *Supported by a grant from Cadence Design Systems, Inc. and by the MARCO Gigascale Silicon Research Center.
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Interconnect Implications of Growth-Based Structural Models for VLSI Circuits* Chung-Kuan Cheng, Andrew B. Kahng and Bao Liu UC San Diego CSE Dept. e-mail:
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Interconnect Implications of Growth-Based Structural Models for VLSI Circuits*
Chung-Kuan Cheng, Andrew B. Kahng and Bao Liu
UC San Diego CSE Dept.
e-mail: {kuan,abk,bliu}@cs.ucsd.edu
*Supported by a grant from Cadence Design Systems, Inc. and by the MARCO Gigascale Silicon Research Center.
Presentation Outline Introduction and Motivation Random Growth Models Experiments Conclusion and Future Work
VLSI circuits:degree d == # adjacent gates
P(d) == # gates with degree d f == # gates being drivenN(f) == # nets with fanout fG == # gatesT == # terminalsE == # crossing edges
(connections between two gates on different sides of a partition)
Definitions
g3
g1
g2
G = 3E = 6T = 4
g3
D(g3) = 5
P(3) += 1
P(5) += 1
P(2) += 1
f = 3N(1) += 2
VLSI Power-Law Phenomena Rent’s rule
pkGT Crossing edge scaling
epeGkE
T == # terminal, G: # gate,
p == Rent exponentE == # connections between two gates on
different sides of the partition
VLSI Power-Law Phenomena (cont.) Vertex degree
dpddkP(d)
Net fanoutfp
f fkN(f) P(d) == # vertices with degree d
d == vertex degree
N(f) == # nets with fanout f
f == net fanout
Power-Law Phenomena in other Contexts Zief’s law
English word frequency with rank i is proportional to i-
Lotka’s law (Yule’s law)# authors (# papers)-2
Power-law vertex degree distribution WWW (in-degree exponent 2.1, out-degree 2.45) actor connectivity (exponent 2.3)paper citation (exponent 3)power grid (exponent 4)
Rent’s Rule Based VLSI Models Claims that Rent’s rule implies fanout distribution
Zarkesh-Ha:Stroobandt-Kurdahi: logistic equations
Are they really correlated?Rent p depends on partitioning method, fanout distribution
does notFamilies of topologies with different p and identical N(f)