Abstract
We propose a class of graphs that would occur naturally in finite-element problems, and we prove a bound on separators for this class of graphs. For three-dimensional graphs, our separator bound is $O(N^{2/3})$. We also propose a simple randomized algorithm to find this separator in $O(N)$ time. Such an algorithm would be used as a preprocessing step for the domain decomposition method of efficiently solving a finite-element problem on a parallel computer. This paper generalizes ``local graphs'''' of Vavasis [1990] to the case of graphs with varying densities of nodes. It also generalizes aspects of Miller and Thurston''s [1990] ``stable graphs.''''
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