Combinatorica
Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
Isoperimetric numbers of graphs
Journal of Combinatorial Theory Series B
SIAM Journal on Computing
Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
Bounds of eigenvalues of preconditioned matrices
SIAM Journal on Matrix Analysis and Applications
Iterative solution methods
On the Quality of Spectral Separators
SIAM Journal on Matrix Analysis and Applications
A Semidefinite Bound for Mixing Rates of Markov Chains
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Performance evaluation of a new parallel preconditioner
IPPS '95 Proceedings of the 9th International Symposium on Parallel Processing
Spectral Partitioning Works: Planar Graphs and Finite Element Meshes
Spectral Partitioning Works: Planar Graphs and Finite Element Meshes
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We introduce the path resistance method for lower bounds on the smallest nontrivial eigenvalue of the Laplacian matrix of a graph. The method is based on viewing the graph in terms of electrical circuits: it uses clique embeddings to produce lower bounds on λ2 and star embeddings to produce lower bounds on the smallest Rayleigh quotient when there is a zero Dirichlet boundary condition. The method assigns priorities to the paths in the embedding; we show that, for an unweighted tree T, using uniform priorities for a clique embedding produces a lower bound on λ2 that is off by at most an O(log diameter(T)) factor. We show that the best bounds this method can produce for clique embeddings are the same as for a related method that uses clique embeddings and edge lengths to produce bounds.