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

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