**2. Circuit partitioning concept**

VLSI circuit partitioning is a vital part of physical design stage. The essence of circuit partitioning is to divide the circuit into a number of sub-circuits with minimum interconnections between them. This can be accomplished by recursively partitioning a circuit into two parts until we reach desired level of complexity. Thus two way partitioning is basic problem in circuit partitioning, which can be described as (Dutt& Deng, 1996).

Logic netlist can be represented as a hypergraph H (V,Eh) where


The problem is:

130 VLSI Design

partitioning. A general graph partitioning though fast, is inefficient while partitioning a tree structure. An algorithm for tree partitioning that can handle large trees with less memory/run time requirement will be a modification of Luke's algorithm. Dynamic program mining based tree partition, which works well for small trees, but because of its high memory and run time complexity, it cannot be used for large trees. In order to optimize above mentioned issues this chapter concentrates on different methodologies starting with Memetic Approach in comparison with genetic concept, Neuro-Memetic approach in comparison with Memetic approach, then deviated the chapter to Neuro EM model with clustering concept. After that the topic concentration is on Fuzzy ARTMAP DBSCAN technique and finally there is a section on Data mining concept using two novel Clustering algorithms achieving the optimality of the partition algorithm in minimizing the number of inter-connections between the cells, which is the required criteria of the partitioning technique in VLSI circuit design. Memetic algorithm (MA) is population based heuristic search approach for combinatorial optimization problems based on cultural evolution. They are designed to search in the space of locally optimal solutions instead of searching in the space of all candidate solutions. This is achieved by applying local search after each of the genetic operators. Crossover and mutation operators are applied to randomly chosen individuals for a predefined number of times. To maintain local optimality, the local search

Neuro-memetic model makes it possible to predict the sub-circuit from circuit with minimum interconnections between them. The system consists of three parts, each dealing with data extraction, learning stage and result stage. In data extraction, a circuit is bipartite and chromosomes are represented for each sub circuit. Extracted sequences are fed to Neuro-memetic model that would recognize sub-circuits with lowest amount of

Next method focuses on the use of clustering k-means (J. B. MacQueen, 1967) and Expectation-Maximization (EM) methodology (Kaban & Girolami, 2000), which divides the circuit into a number of sub-circuits with minimum interconnections between them, and partition it into 10 clusters, by using k-means and EM methodology. In recognition stage the parameters, centroid

Further, a new model for partitioning a circuit is explored using DBSCAN and fuzzy ARTMAP neural network. The first step is concerned with feature extraction, where it uses DBSCAN algorithm. The second step is classification and is composed of a fuzzy ARTMAP

Finally, two clustering algorithms Nearest Neighbor (NNA) and Partitioning 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

VLSI circuit partitioning is a vital part of physical design stage. The essence of circuit partitioning is to divide the circuit into a number of sub-circuits with minimum

into the existing clusters that are closest. PAM represents a cluster by a medoid.

and probability are fed into generalized delta rule algorithm separately.

procedure is applied to the newly created individuals.

interconnections between them.

**2. Circuit partitioning concept** 

neural network.

