Combinatorica
The isoperimetric number of random regular graphs
European Journal of Combinatorics
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Isoperimetric numbers of graphs
Journal of Combinatorial Theory Series B
Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
On the second eigenvalue of a graph
Discrete Mathematics
Existence and explicit constructions of q+1 regular Ramanujan graphs for every prime power q
Journal of Combinatorial Theory Series B
On the performance of spectral graph partitioning methods
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Spectral partitioning works: planar graphs and finite element meshes
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Survey: The cook-book approach to the differential equation method
Computer Science Review
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The communication overhead is a major bottleneck for the execution of a process graph on a parallel computer system. In the case of two processors, the minimization of the communication can be modeled by the graph bisection problem. The spectral lower bound of λ2|V|/4 for the bisection width of a graph is well-known. The bisection width is equal to λ2|V|/4 iff all vertices are incident to λ2/2 cut edges in every optimal bisection. We discuss the case for which this fact is not satisfied and present a new method to get tighter lower bounds on the bisection width. This method makes use of the level structure defined by the bisection. Under certain conditions we get a lower bound depending on λ2β|V| with 1/2 ≤ β