  We investigate the problem of computing the shortest secure path in a Voronoi
diagram. Here, a path is secure if it is a sequence of touching Voronoi cells,
where each Voronoi cell in the path has a uniform cost of being secured.
Importantly, we allow inserting new sites, which in some cases leads to
significantly shorter paths. We present an $O(n \log n)$ time algorithm for
solving this problem in the plane, which uses a dynamic additive weighted
Voronoi diagram to compute this path. The algorithm is an interesting
combination of the continuous and discrete Dijkstra algorithms. We also
implemented the algorithm using CGAL.
