# Lec26 - Partitioning Lec 26 Algorithm (Kernighan-Lin algo)...

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Partitioning Lec 26

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Algorithm (Kernighan-Lin algo)
Steps Convert the circuit into a graph. To do this, each gate is treated as a vertex of the graph. If two gates are directly connected by a net, then an edge is placed between the corresponding vertices of the graph.

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The initial partition is generated “at random.” We create two subcircuits S1, and S2. If the circuit has n gates, the first n/2 are assigned to S1, and the rest are assigned to S2.
The goodness of a solution is equal to the number of graph edges that are cut. Suppose the edge (V,W) exists in the graph derived from the circuit. If V and W are in different subcircuits, we say that the edge (V,W) is cut. Otherwise we say that (V,W) is uncut.

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The technique for generating new solutions from old solutions is to select a subset of gates from S1, and a subset of gates from S2 and swap them. To maintain acceptability, we always select two subsets of the same size.
Compute the total no of cut nets in the circuit and record it as ”zero swaps” count. Compute the cut (Cv) and uncut (Uv) counts of each vertex. Cv + Uv = degree of V. (total no. of edges connected to V.) Temporary swapping of a pair of gates one at a time until min-cut is achieved. Compute the improvement

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## This note was uploaded on 05/08/2010 for the course EEE SSM taught by Professor Pawansharma during the Spring '10 term at Birla Institute of Technology & Science.

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Lec26 - Partitioning Lec 26 Algorithm (Kernighan-Lin algo)...

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