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kernlin

# kernlin - Kernighan-Lin Graph Distance Metrics 858L...

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Kernighan-Lin, Graph Distance Metrics 858L

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Kernighan-Lin Graph Partitioning
Kernighan-Lin Graph Partitioning Problem . Divide a weighted graph with 2n nodes into two parts, each of size n , to minimize the sum of the weights crossing the two parts. You could just use minimum cut if you didn’t have the restriction to each part being of size n. Idea (Kernighan-Lin, 1970): start with some partition that satisfies the size requirement and repeatedly swap nodes between the partitions.

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Kernighan-Lin More Detail Repeat until no more vertices are left: Divide the network into 2 parts A, B of equal size arbitrarily. Select a i A, b i B, such that the reduction in cost is as large as possible and neither a i , b i has been chosen before Let C i be the cost of the partition after swapping a i ,b i Swap a i and b i Return (A’,B’) corresponding to the smallest C i observed. While cost continues to be reduced Call using the returned partition as the new starting point
Improving this Solution A B Find the optimal partitions in A and B separately A’ B’ B’’ A’’ Run KL procedure on all 3 of these starting partitions

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Three KL Extensions (1) Divide into partitions of unequal (but known) sizes: Start with a partition that satisfies the sizes you want. Stop when all the nodes on the smaller side have been swapped.
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kernlin - Kernighan-Lin Graph Distance Metrics 858L...

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