Abstract In this article, the effective circuit partitioning techniques are employed by using the clustering algorithms. The technique uses the circuit netlist in order to cluster the circuit in partitioning steps and it also minimizes the interconnection distance with the required iteration level. The clustering algorithm like K-Mean, Y-Mean, K-Medoid are performed on the standard benchmark circuits. The results obtained shows that the proposed techniques improves the time and also minimize the area by reducing the interconnection distance

R Manikandan

V Leela

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Contemporary Engineering Sciences, Vol. 7, 2014, no. 19, 923 - 929 
HIKARI Ltd,  www.m-hikari.com 
http://dx.doi.org/10.12988/ces.2014.4653 
 
 
Effective Clustering Algorithms for VLSI Circuit   
 
Partitioning Problems 
 
R. Manikandan 
 
School of Computing 
SASTRA University 
Thanjavur-613401, India 
 
V. Leela 
 
School of Computing 
SASTRA University 
Thanjavur-613401, India 
 
   Copyright © 2014 R. Manikandan and V. Leela. This is an open access article distributed 
under the Creative Commons Attribution License, which permits unrestricted use, distribution, and 
reproduction in any medium, provided the original work is properly cited. 
 
Abstract 
 
In this article, the effective circuit partitioning techniques are employed by using 
the clustering algorithms. The technique uses the circuit netlist in order to cluster 
the circuit in partitioning steps and it also minimizes the interconnection distance 
with the required iteration level. The clustering algorithm like K-Mean, Y-Mean, 
K-Medoid are performed on the standard benchmark circuits. The results obtained 
shows that the proposed techniques improves the time and also minimize the area 
by reducing the interconnection distance. 
 
Keywords: Cluster, K-Mean, Y-Mean, K-Medoid, VLSI Circuit partitioning 
  
 
1 Introduction 
 
       The circuit partitioning plays the dominant role in the VLSI physical 
design. The partitioning steps used to minimize the larger circuit into smaller 
circuit. The main goal of partitioning is to identify the strongly connected cells in 
order to minimize the connected distance among the cells. Similarly the clustering 
is used to cluster the objects which are similar within the group and different from  
924                                      R. Manikandan and V. Leela 
 
 
the objects present in other group. The cluster partition the circuit into non 
overlapping subsets [2]. The clustering algorithm are used in various applications 
like market research, security and physical geography.  
 
In this paper the standard benchmark circuit are taken for partitioning techniques 
with the clustering algorithm like K-Mean,Y-Mean and Fuzzy c mean. The netlist 
of the benchmark circuit are taken as input and the matrix are generated in order 
to cluster the circuit based on the gate distance matrix. The output obtained from 
the algorithm allows to discuss the clustering algorithm performance and also 
gives the beneficial output with the reduction in time and interconnection distance.  
local optimization problem was also reduced in circuit partitioning  
 
 
2 Clustering Techniques 
  
  The clustering is an active approach for exploring the common metric 
similarities within the data and making them as groups. Every Clustering 
techniques, nominates the clustered data set into numerous groups such that the 
common features among the group is maximum when compared to other groups 
[9]. The process of data clustering is simple with few sets of data but when its a 
large amount of data, it has to be categorized into small number of groups to 
analyze the performance. 
 
2.1 K –Means 
 
        K-Means is one of the simplest methods among all partitioning based 
data clustering methods. It segments the circuit into k clusters, where k is the 
number of user desired clusters and defined by the user. Every cluster are assigned 
with centroids. All the data sets are set in a cluster having centroid nearest to that 
data object. In each iteration centroids change their location step by step. This 
process is continued until centroid are stable at place [6] . 
Step 1: Assign the random values for cluster Centre and start the process by 
selecting the clusters in data. 
Step 2: Calculate the assigned values of the matrix function by Equation (1). 
         
Step 3: Evaluate the centroid of the data using the Equation (1). Then compare 
the value if it is less than tolerance value or below a threshold value ,then stop the 
function. 
Step 4: Apprise the values of the centers according equation (2).and  move  to 
step 2. 



gixk
xk
gi
ci
||
1
 
----- (1) 
-------(2) 
Effective clustering algorithms                                     925 
 
 
2.2 Fuzzy C Mean  
 
Fuzzy C-Means clustering (FCM), is the data clustering algorithm in which each 
data set belongs to a cluster to a degree assigned by a membership [8] .This 
techniques works iteratively until no further clustering is possible. Fcm undergoes 
following techniques for centroid calculations [10] . 
Step 1: Assign the process randomly in matrix U within 1 by estimating in 
Equation (3)are satisfied. 
           
                           



c
i
njuij
1
.,...1,1
 
Step 2: Estimate cluster points in centers assigned in fuzzy using Equation (4). 
              
xj
uij
uij
ci
n
j
n
j





1
1
            
Step 3: Calculate the cluster centroids function and check the values ,if it is below 
the tolerance or threshold value then terminate the function. 
               
                    
 

c
i
n
j
c
i
u i j d i jjiccuj
1 1
2
1
),...1,(  
Step 4: Update new matrix function by u and estimate the cluster from step 2. 
                         



c
k d k j
dy
uij
1
1
k=0,1..n. 
2.3 Y -Means  
           In order to overcome the drawbacks of K means algorithm ,Y-means 
clustering established. The basic Y-mean clustering undergoes the following 
process. As the initial process it allows the self  defined cluster value k, then it 
undergoes the following process as like K means in order to detect the 
centroids ,then it checks for degeneracy ,if its found it removes the empty cluster 
else undergoes splitting and merging action [7]. The number of clusters is 
adjusted by removing empty clusters as well as merging and linking existing 
clusters. Due to the fact that the final number of clusters is independent of initial k. 
But it has the time complexity and iteration steps when the data sets are high. In 
order to overcome the drawbacks of basic Y-mean algorithm, Improved Y-Mean 
clustering techniques are employed in circuit clustering [1] and process are 
followed 
Step 1:Initialize the size of the cluster Ci by (n/k)=S, where n is the no of data 
points and k is the cluster size. 
Step 2:Create the array Bk and include all the Ak(data array) to Bk until the value 
is equal to Ci Cluster.  
----(3) 
-----(4) 
------(5) 
-----(6) 
926                                      R. Manikandan and V. Leela 
 
 
Step 3: Compute the arithmetic mean function M and compare the initial cluster 
value with the new data    points.ie i<k<j 
 
i
idj
a
k
i i
CD
CK
I
M 


1 ||||
1
 
 
Step 4: Compute the distance D of all A  to M of Initial Clusters Cj  If Akof 
Dkand M is less than or equal to other distances then remain in same cluster else 
undergoes merging and splitting techniques with centroids by   the gaussian 
distribution is given by 
 
2
2
2
)(
2
1
)(






x
exf  
 
Step 5:Recompute M and move to BK until there exit no change in clusters . 
 
 
 
3 Experimental Results 
 
The circuit clustering of the standard benchmark circuit netlists are taken in the 
format of spice netlist. Then the input file to Turbo C+ is given with netlist of 
various circuit in order to generate the connectivity matrix which gives the 
essential distance based gate based upon their connections. The matrix format of 
the output file is processed for circuit clustering techniques through 
K-mean,Y-mean and fuzzy-c mean algorithm [4]. 
 
          The ISPD98 benchmark suite is chosen asthe test circuits. The circuit 
clustering is performed using Matlab 2010A.The table 1 shows the net cuts of the 
circuit obtained from the clustering algorithm. The table 2 shows the runtime and 
the accuracy's obtained from the clustering algorithm. The figure 1 gives the 
comparison between the three algorithm in performance based in circuit clustering. 
The Y mean has the higher iteration along with Fuzzy C mean for the 
performance. The circuit are clustered by reducing the interconnection distance 
among the gates, where it identifies the similar subset among the gates in order to 
minimize the larger circuit into smaller circuit. The local optimization problem of 
the clustering algorithm were also minimized [5] . 
 
 
 
 
 
-----(8) 
------(7) 
Effective clustering algorithms                                     927 
 
 
Circuit      K-mean Y-mean Fuzzy 
c-mean 
 
net cut net cut net cut 
ibm01 216 213 215 
ibm02 254 262 250 
ibm03 779 741 735 
ibm04 438 440 437 
ibm05 1714 1769 1765 
ibm06 364 367 365 
ibm07 719 734 729 
ibm08 1150 1143 1152 
ibm09 521 523 519 
ibm10 757 752 753 
 
             Table 1.The net cut of the clustering algorithm in benchmark circuit 
 
 
 
circuit K-mean Y-mean Fuzzy c-mean 
 
R A R A R A 
ibm01 1.3 82 1.2 85 2 86 
ibm02 1.2 81 1.1 84 1,9 85 
ibm03 1.7 83 1.5 85 2.7 86 
ibm04 1.5 84 1.3 84 3 87 
ibm05 2 84 1.4 86 4 88 
ibm06 2.7 82 2 84 3.4 85 
ibm07 4 79 3.5 82 4.7 84 
ibm08 4.5 80 4 83 6 89 
ibm09 3.5 81 3.3 85 5.4 87 
ibm10 5.7 84 4 86 5.8 89 
 
*R-Runtime; *A-Accuracy 
Table2.The performance analysis of clustering algorithm with benchmark circuit 
 
928                                      R. Manikandan and V. Leela 
 
 
1 2 3 4 5 6 7
0
2
4
6
8
10
12
14
16
18
Plot of Iteration over Time
I
t
e
r
a
t
io
n
 
 Run Time (s)
 
 
K mean
fuzzy c mean
y mean
 
Fig.1.The plot of iteration over time of clustering algorithm. 
 
 
4 Conclusion 
 
The circuit clustering of the ISPD98 benchmark circuit is partitioned using the 
clustering algorithm in order to minimize the interconnection distance and also 
reduce to the time of partitioning. Thus the Fuzzy-c mean gives the accurate result 
when we compared to other two algorithm but increases the run time [3]. Y-mean 
has less runtime because of trained sets. 
     The distance based matrix sets are given for data generation of clustering 
algorithm. The local optimum problem is also reduced when compared to other 
clustering algorithm with following data sets. 
 
 
References 
 
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k-mean and y-means algorithms in fisher’s iris data sets” International Journal of 
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[3] Khalid Hammouda, Prof. Fakhreddine Karray,”A Comparative Study of Data 
Clustering Techniques”, University of Waterloo, Ontario, Canada N2L 3G1. 
Effective clustering algorithms                                     929 
 
 
[4] Rachitha Sony Krotha, Suneetha Merugula”A Brief Survey On Document 
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[7] H.S. Park , C.H. Jun, A simple and fast algorithm for K-medoids clustering, 
Expert Systems with Applications, 36(2):2009, 3336–3341. 
[8] Peter J. Rousseeuw, Silhouettes: a graphical aid to the interpretation and 
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[9] Seyed Mohammad Razavi Zadegan, Mehdi Mirzaie, Farahnaz Sadoughi, 
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Received: June 11, 2014 
 
 


Effective Clustering Algorithms for VLSI Circuit Partitioning Problems

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Effective Clustering Algorithms for VLSI Circuit Partitioning Problems

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