Improving shortest paths in the Delaunay triangulation

We study a problem about shortest paths in Delaunay triangulations. Given two nodes s; t in the Delaunay triangulation of a point set P, we look for a new point p that can be added, such that the shortest path from s to t in the Delaunay triangulation of P u{p} improves as much as possible. We study properties of the problem and give efficient algorithms to find such a point when the graph-distance used is Euclidean and for the link-distance. Several other variations of the problem are also discussed.

Quantifying dispersal paths in probabilistic habitat networks: a reply to hock and mumby (2015) and an overview of recent developments and applications

Hock and Mumby (2015) describe an approach to quantify dispersal probabilities along paths in networks of habitat patches. This approach basically consists in determining the most probable (most reliable) path for movement between habitat patches by calculating the product of the dispersal probabilities in each link (step) along the paths in the network. Although the paper by Hock and Mumby (2015) has value and includes interesting analyses (see comments in section 7 below), the approach they describe is not new.