  The Outerplanar Diameter Improvement problem asks, given a graph $G$ and an
integer $D$, whether it is possible to add edges to $G$ in a way that the
resulting graph is outerplanar and has diameter at most $D$. We provide a
dynamic programming algorithm that solves this problem in polynomial time.
Outerplanar Diameter Improvement demonstrates several structural analogues to
the celebrated and challenging Planar Diameter Improvement problem, where the
resulting graph should, instead, be planar. The complexity status of this
latter problem is open.
