k-Pairs Non-Crossing Shortest Paths in a Simple Polygon

This paper presents an O(n+k) time algorithm to compute the set of k non-crossing shortest paths between k source-destination pairs of points on the boundary of a simple polygon of n vertices. Paths are allowed to overlap but are not allowed to cross in the plane. A byproduct of this result is an O(n) time algorithm to compute a balanced geodesic triangulation which is easy to implement. The algorithm extends to a simple polygon with one hole where source destination pairs may appear on both the inner and outer boundary of the polygon. In the latter case, the goal is to compute a collection of non-crossing paths of minimum total cost.