  We present a new algorithm for computing the straight skeleton of a polygon.
For a polygon with $n$ vertices, among which $r$ are reflex vertices, we give a
deterministic algorithm that reduces the straight skeleton computation to a
motorcycle graph computation in $O(n (\log n)\log r)$ time. It improves on the
previously best known algorithm for this reduction, which is randomized, and
runs in expected $O(n \sqrt{h+1}\log^2 n)$ time for a polygon with $h$ holes.
Using known motorcycle graph algorithms, our result yields improved time bounds
for computing straight skeletons. In particular, we can compute the straight
skeleton of a non-degenerate polygon in $O(n (\log n) \log r +
r^{4/3+\varepsilon})$ time for any $\varepsilon>0$. On degenerate input, our
time bound increases to $O(n (\log n) \log r + r^{17/11+\varepsilon})$.
