PLANAR SEPARATORS AND PARALLEL POLYGON TRIANGULATION

We show how to construct an O(root n)-separator decomposition of a pla nar 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(root n) -separator of that subgraph. We also show how to construct an O(n(epsi lon))-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(12+epsilon))-se parator of that subgraph. We demonstrate the utility of such a separat or decomposition by showing how it can be used in the design of a para llel algorithm for triangulating a simple polygon deterministically in O(log n) time using O(n/log n) processors on a CRCW PRAM. (C) 1995 Ac ademic Press, Inc.