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Traditionally, the quality of orthogonal planar drawings is quantified by the total number of bends or the maximum number of bends per edge. However, this neglects that, in typical applications, edges have varying importance. We consider the problem OptimalFlexDraw that is defined as follows....
The input to the NP-hard point line cover problem (PLC) consists of a set P of n points on the plane and a positive integer k; the question is whether there exists a set of at most k lines that pass through all points in P. By straightforward reduction rules, one can efficiently reduce any input...
It is long known that for every weighted undirected n-vertex m-edge graph G = (V, E, ), and every integer k 1, there exists a ((2k 1) (1 + ))-spanner with O(n1 + 1/k) edges and weight O(k n1/k (MST(G)), for an arbitrarily small constant > 0. (Here (MST(G)) stands for the weight of the...
We investigate the combinatorial complexity of geodesic Voronoi diagrams on polyhedral terrains using a probabilistic analysis. Aronov et al.  prove that, if one makes certain realistic input assumptions on the terrain, this complexity is (n+m√n) in the worst case, where n denotes the...
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