New Probabilistic Algorithm for VLSI Circuit Partitioning - Prof. Shantanu S. Dutt, Study notes of Electrical and Electronics Engineering

Download New Probabilistic Algorithm for VLSI Circuit Partitioning - Prof. Shantanu S. Dutt and more Study notes Electrical and Electronics Engineering in PDF only on Docsity! A ProbabilityBased Approach to VLSI Circuit Partitioning Shantanu Dutt and Wenyong Deng
Department of Electrical Engineering University of Minnesota Minneapolis Minnesota




LSI Logic Corporation Milpitas CA 

OUTLINE Problem Denition Previous Partitioning Methods Previous Iterative Improvement Methods The New ProbabilityBased Partitioner PROP Potential Node Gain Computation Probability Computation Results Conclusions
IterativeImprovement Algorithms The KL FM Algorithm The gain of a node u say in V is dened as gainu
 X niEu cni

X njIu cnj
Eu is the set of cutset nets connected only to u in V Iu is the set of nets connected to u that are not in the cutset The gain can be positive or negative n1 n2 Cutset V2 n3 n4 V1 u Eu = {n1, n2} Iu = {n4} gain(u) = 2 − 1 = 1  The KL FM Algorithm Contd  Generate an initial partition Pick best unlocked node among both subsets to move if the balance condition egs 


 is met Otherwise pick best unlocked node to move from the other subset  Tentatively move and lock the node  Update gains of the neighbors of swapped node
Repeat steps  until all nodes are locked  Compute the prex sums Sus of gains of all nodes u in order of move Actually perform swaps till node x s t Sx is the highest 2 0 1 −2 3 −2 −1 5 −2 −4 −7 2 2 2 1 4 2 1 6 4 0 −7 Gain of moved nodes Prefix Sum Make actual moves till this point  If Sx  new partition  swapped partition repeat steps  else new partition  old partition exit  The Lookahead LA Algorithm Krishnamurthy IEEE Trans Comput May  Each node has a gain vector gainu
k of node u with k elements k is the degree of lookahead Assume u  V The ith element of the gain vector   i  k gainu
i   of nets in the cutset that are connected to i nodes in V including u   of nets in the cutset connected to u that have i
 nodes in V
n1 n2 Cutset V2 n3 n4 V1 u gain(u)[1] = 2−1 = 1 gain(u)[2] = −2 gain(u)[3] = 2−1 = 1 Generally best performance is obtained for k   to  Memory requirement is pkmax
 PROP Determining Node Probabilities  Either a Compute deterministic gains of nodes according to FM and using a function fgu

assign node probabilities OR b Assign a xed probability of say   to each node Iterate the following steps  or more times  Compute probabilistic gains gniu
corresponding to each net ni connected to u and then its total gain gu
 P uni gniu
 Assign probabilities using fgu

PROP Determining Node Probabilities Contd Cutset 1 2 3 4 5 6 7 8 9 10 11 n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14 n15 n16 n17 V2 V1 2, 1 2, 1 2, 1 1, 0.8 1, 0.8 −1, 0.2 −1, 0.2 −1, 0.2 −1, 0.2 −1, 0.2 −1, 0.2 g(1), p(1) Cutset 1 2 3 4 5 6 7 8 9 10 11 n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12 n13 n14 n15 n16 n17 V2 V1 1.8, 0.9 1.8, 0.92.64, 1 g(1), p(1) −.49, 0.3 −.49, 0.3 −.49, 0.3 −.49, 0.3 −0.3, 0.4 −0.3, 0.4 2.0016, 1 2.04, 1 (a) 1st Iteration (b) 2nd Iteartion PROP Contd The rest of the algorithm is as follows  Pick unlocked node with highest gu
among both subsets to move if the balance condition is met Otherwise pick best un locked node to move from the other subset Tentatively move and lock the node Note the immediate move gain  Update probabilities of nets connected to moved node and the gains of its neighbors  Repeat steps  until all nodes are locked
Compute the prex sums Sus of gains of all nodes u in order of move Actually perform swaps till node x s t Sx is the highest  If Sx  new partition  swapped partition repeat steps 
else new partition  old partition exit
PROP is Not Only a TieBreaking Extension of FM It is a completely new gain calculation method Cutset 0.5 0.5 0.8 1 1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.99 1.98 1.79 0.7 0.7 p(u) g(u) FM 2 FM 3 FM 1 FM 0 FM 0 FM−gain  Calculating Node Probabilities Need a monotonically increasing function of node gains gu
s A caveat that works well is applying thresholding gup say  
glow say    on node gains Probabilities of all other nodes are computed using the probability function g low g up p max p minP ro ba bi lit ie s Gains Semi−Gaussian Linear  Time and Space Complexities Initial probability and gain calculations Ond
Choosing the best node takes constant time thus total of n
for entire pass Updating p nets and d neighbors per moved node takes time p d
 total is nd
Reinsertion of each neighbors in the balanced binary search tree takes logn time total updation time is nd logn
Thus time complexity of PROP is nd logn
Space complexity is nd
net and node incidence lists