  We are given a read-only memory for input and a write-only stream for output.
For a positive integer parameter s, an s-workspace algorithm is an algorithm
using only $O(s)$ words of workspace in addition to the memory for input. In
this paper, we present an $O(n^2/s)$-time $s$-workspace algorithm for
subdividing a simple polygon into $O(\min\{n/s,s\})$ subpolygons of complexity
$O(\max\{n/s,s\})$.
  As applications of the subdivision, the previously best known time-space
trade-offs for the following three geometric problems are improved immediately:
(1) computing the shortest path between two points inside a simple $n$-gon, (2)
computing the shortest path tree from a point inside a simple $n$-gon, (3)
computing a triangulation of a simple $n$-gon. In addition, we improve the
algorithm for the second problem even further.
