A graph contraction algorithm for the fast calculation of the Fiedler vector of a graph

Conference · Fri Dec 01 04:00:00 EST 1995

OSTI ID:125587

Driessche, R Van; Roose, D ^[1]

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1. Katholieke Universiteit Leuven, Heverlee (Belgium)

The spectral bisection algorithm bisects a graph into equally-sized parts in such a way that only a near minimal number of edges is cut. It requires the calculation of the Fiedler vector of the graph, i.e. the eigenvector that corresponds to the second smallest eigenvalue of the Laplacian matrix. Traditionally, a Lanczos algorithm is used for this purpose. Barnard and Simon have proposed calculating the Fiedler vector with a multilevel algorithm. This requires the construction of a series of consecutively smaller contractions of the graph. In this paper, we present a powerful graph contraction algorithm. We will show that the Fiedler vector of a contracted graph is a very good approximation of the Fiedler vector of the original graph and that the resulting multilevel algorithm calculates the Fiedler vector in less time than a Lanczos algorithm.

• OSTI ID: 125587
• Report Number(s): CONF-950212--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
EFFICIENCY
FACTORIZATION
MATRICES
PARALLEL PROCESSING
TASK SCHEDULING