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Journal Articles SIAM Journal on Scientific Computing Year : 1997

On the optimality of the median cut spectral bisection graph partitioning method

Tony F. Chan
  • Function : Author
W. K. Szeto
  • Function : Author

Abstract

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 $s\ge1$, to the second eigenvector. Moreover, we prove that the same result also holds for any m-partition, that is, a partition into m and (n-m)$ vertices, when using the mth largest or smallest components of the second eigenvector. Copyright © 1997 Society for Industrial and Applied Mathematics
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hal-01010396 , version 1 (19-06-2014)

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Tony F. Chan, Patrick Ciarlet, W. K. Szeto. On the optimality of the median cut spectral bisection graph partitioning method. SIAM Journal on Scientific Computing, 1997, 18 (3), pp.943-948. ⟨10.1137/S1064827594262649⟩. ⟨hal-01010396⟩
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