Shortest Secure Path in a Voronoi Diagram

07/19/2020

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by   Sariel Har-Peled, et al.

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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.