Let G be an embedded planar graph whose edges may be curves. For two arbitrary points of G, we can compare the length of the shortest path in G connecting them against their Euclid...
An orthogonal spanner network for a given set of n points in the plane is a plane straight line graph with axis-aligned edges that connects all input points. We show that for any ...
Given a set S of n points in RD , and an integer k such that 0 k < n, we show that a geometric graph with vertex set S, at most n − 1 + k edges, maximum degree five, and dila...
Boris Aronov, Mark de Berg, Otfried Cheong, Joachi...
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 ...