Abstract
We present a randomized O(nlog log n) time algorithm for constructing a recursive separator decomposition for well-shaped meshes in two and three dimensions. Our algorithm takes O(nlog log n) time while previous algorithms require $\Theta$(nlog n) time. It uses techniques from probability theory, computational geometry, and graph theory. The new algorithm has an application in the solution of sparse linear systems that arise in finite element calculations. In particular, it can be used to design O(nlog log n) time algorithms for finding a provably good nested-dissection ordering for 3D finite element systems. It can also be used to improve the construction of 3D point location structures, which are useful in hierarchical methods such as the multigrid and multilevel domain decompositions.
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