Planar Separators and Parallel Polygon Triangulation

We show how to construct an O p n separator decomposition of a planar graph G in O n time Such a decomposition de nes a binary tree where each node corresponds to a subgraph of G and stores an O p n separator of that subgraph We also show how to construct an O n way decomposition tree in parallel in O log n time so that each node corresponds to a subgraph of G and stores an O n separator of that subgraph We demonstrate the utility of such a separator decomposition by showing how it can be used in the design of a parallel algorithm for triangulating a simple polygon deterministically in O log n time using O n log n processors on a CRCW PRAM