Planar separators and parallel polygon triangulation

Abstract

We show how to construct an O(√n)-separator decomposition of a planar graph G in O(n) time. Such a decomposition defines a binary tree, where each node corresponds to a subgraph of G and stores an O(√n)-separator of that subgraph. We also show how to construct an 0(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(n12 - ∈)-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. © 1995 Academic Press, Inc.