2 research outputs found
Essential Constraints of Edge-Constrained Proximity Graphs
Given a plane forest of points, we find the minimum
set of edges such that the edge-constrained minimum spanning
tree over the set of vertices and the set of constraints contains .
We present an -time algorithm that solves this problem. We
generalize this to other proximity graphs in the constraint setting, such as
the relative neighbourhood graph, Gabriel graph, -skeleton and Delaunay
triangulation. We present an algorithm that identifies the minimum set
of edges of a given plane graph such that for , where is the
constraint -skeleton over the set of vertices and the set of
constraints. The running time of our algorithm is , provided that the
constrained Delaunay triangulation of is given.Comment: 24 pages, 22 figures. A preliminary version of this paper appeared in
the Proceedings of 27th International Workshop, IWOCA 2016, Helsinki,
Finland. It was published by Springer in the Lecture Notes in Computer
Science (LNCS) serie