**8.4 Nearest Neighbor and Partitioning Around Medoids clustering Algorithms**

Two clustering algorithms Nearest Neighbor (NNA) and Partitoning Around Medoids (PAM) clustering algorithms are considered for dividing the circuits into sub circuits. Clustering is alternatively referred to as unsupervised learning segmentation. The clusters are formed by finding the similarities between data according to characteristics found in the actual data. NNA is a serial algorithm in which the items are iteratively merged into the existing clusters that are closest. PAM represents a cluster by a medoid.


As the number of clusters increases, the time taken for PAM increases but is less than Nearest Neighbor algorithm. PAM performs better than Nearest Neighbor algorithm. PAM has been very competent, especially in the case of a large number of cells when compared with Nearest Neighbor. The proposed model based algorithm has achieved sub-circuits with minimum interconnections, for the Circuit Partitioning problem.

Algorithms for CAD Tools VLSI Design 163

Fig. 30. Graph depicting CPU utilization of NNA, PAM, algorithm proposed in (Gerez, 1999)

From the implementation of the two algorithms, Nearest Neighbor and Partitioning Around Medoids, some fundamental observations are made. There is a reduction of 1 interconnection when a circuit with 8 nodes is partitioned and when a circuit with 15 nodes is partitioned, there is a reduction of 5 interconnections between the sub-circuits obtained using NNA and PAM. Therefore, it is concluded that the number of nodes in a circuit and the number of interconnections are inversely proportional. That is, as the number of nodes in a circuit increases, the number of interconnections between sub-circuits decreases for both partitioning methods. This reduction is not consistent since the complexity of any circuit will not be known a priori. One of the future enhancements would be to analyze the percentage ratio of the number of nodes in a circuit to the number of interconnections that

Future enhancements envisaged are using of distance based classification data mining concepts and other data mining concepts, Artificial/ Neural modeled algorithm in getting

I would like to acknowledge my profound gratitude to the Management, Rashtreeya Sikshana Samithi Trust, Bangalore.I am indebted to Dr. S.C. Sharma, Vice Chancellor, Tumkur University, Karnataka for his unending support.I would like to thank all my official colleagues at R V College of Engineering and specifically the MCA department staffs for their remarkable co-ordination. Last but not the least, I would like to thank my family

over number of iterations

get reduced after the circuit is partitioned.

**9. Future enhancements** 

better optimized partitions.

**10. Acknowledgement** 

members.


Table 4. Comparison of time taken to partition using PAM and Nearest Neighbor

Completion time: Graphs depict completion time increases proportionately with respect of number of clusters. Nearest neighbor algorithm takes more completion time as number of iterations increase when compared to PAM.

Fig. 29. Graph depicting the Completion time of NNA and PAM compared with algorithm proposed in (Gerez, 1999) over number of clusters

CPU Utilization: A graph depicts CPU utilization increases proportionately with respect of number of iterations. PAM takes less CPU utilization as number of iteration increase compared to NNA algorithm.

PAM Nearest Neighbor

Completion time: Graphs depict completion time increases proportionately with respect of number of clusters. Nearest neighbor algorithm takes more completion time as number of

Fig. 29. Graph depicting the Completion time of NNA and PAM compared with algorithm

CPU Utilization: A graph depicts CPU utilization increases proportionately with respect of number of iterations. PAM takes less CPU utilization as number of iteration increase

Clusters Time taken(Secs)

Table 4. Comparison of time taken to partition using PAM and Nearest Neighbor

2 0.045 0.5 4 0.067 0.7 6 0.075 0.8 8 0.087 0.9

No. of

iterations increase when compared to PAM.

proposed in (Gerez, 1999) over number of clusters

compared to NNA algorithm.

Fig. 30. Graph depicting CPU utilization of NNA, PAM, algorithm proposed in (Gerez, 1999) over number of iterations

From the implementation of the two algorithms, Nearest Neighbor and Partitioning Around Medoids, some fundamental observations are made. There is a reduction of 1 interconnection when a circuit with 8 nodes is partitioned and when a circuit with 15 nodes is partitioned, there is a reduction of 5 interconnections between the sub-circuits obtained using NNA and PAM. Therefore, it is concluded that the number of nodes in a circuit and the number of interconnections are inversely proportional. That is, as the number of nodes in a circuit increases, the number of interconnections between sub-circuits decreases for both partitioning methods. This reduction is not consistent since the complexity of any circuit will not be known a priori. One of the future enhancements would be to analyze the percentage ratio of the number of nodes in a circuit to the number of interconnections that get reduced after the circuit is partitioned.
