## Planar Separators and Parallel Polygon Triangulation

Citations: | 53 - 8 self |

### BibTeX

@MISC{Goodrich_planarseparators,

author = {Michael T. Goodrich},

title = {Planar Separators and Parallel Polygon Triangulation},

year = {}

}

### OpenURL

### Abstract

We show how to construct an O ( p 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 ( 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 1=2+)-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.