# 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}
}```
• Published 1 May 1997
• Mathematics, Computer Science
• SIAM J. Sci. Comput.
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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