We propose a geometric constraint solving method based on connectivity analysis in graph theory, which can be used to decompose a well-constrained problem into some smaller ones i...
Let G be a connected plane geometric graph with n vertices. In this paper, we study bounds on the number of edges required to be added to G to obtain 2-vertex or 2-edge connected ...
We consider the problem of constructing bounded-degree planar geometric spanners of Euclidean and unit-disk graphs. It is well known that the Delaunay subgraph is a planar geometri...
We prove that computing a geometric minimum-dilation graph on a given set of points in the plane, using not more than a given number of edges, is an NP-hard problem, no matter if ...
We give a simple proof for a theorem of Katchalski, Last, and Valtr, asserting that the maximum number of edges in a geometric graph G on n vertices with no pair of parallel edges...