On the Optimality of the Median Cut Spectral Bisection Graph Partitioning Method

@article{Chan1997OnTO,
  title={On the Optimality of the Median Cut Spectral Bisection Graph Partitioning Method},
  author={Tony F. Chan and Patrick Ciarlet and W. K. Szeto},
  journal={SIAM J. Sci. Comput.},
  year={1997},
  volume={18},
  pages={943-948}
}
Recursive spectral bisection (RSB) is a heuristic technique for finding a minimum cut graph bisection. To use this method the second eigenvector of the Laplacian of the graph is computed and from it a bisection is obtained. The most common method is to use the median of the components of the second eigenvector to induce a bisection. We prove here that this median cut method is optimal in the sense that the partition vector induced by it is the closest partition vector, in any ls norm, for $s… 
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