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» Three-Clustering of Points in the Plane
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GD
2006
Springer
14 years 1 months ago
Computing Geometric Minimum-Dilation Graphs Is NP-Hard
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 ...
Rolf Klein, Martin Kutz
CCCG
2007
13 years 11 months ago
Hamilton Circuits in Hexagonal Grid Graphs
We look at a variant of the Hamilton circuit problem, where the input is restricted to hexagonal grid graphs. A hexagonal grid graph has a vertex set that is a subset of the grid ...
Kamrul Islam, Henk Meijer, Yurai Núñ...
CCCG
2008
13 years 11 months ago
The Steiner Ratio for Obstacle-Avoiding Rectilinear Steiner Trees
We consider the problem of finding a shortest rectilinear Steiner tree for a given set of points in the plane in the presence of rectilinear obstacles that must be avoided. We ext...
Mina Razaghpour, Anna Lubiw
CCCG
2006
13 years 11 months ago
A Study of Conway's Thrackle Conjecture
A thrackle is a drawing of a simple graph on the plane, where each edge is drawn as a smooth arc with distinct end-points, and every two arcs have exactly one common point, at whi...
Wei Li 0011, Karen Daniels, Konstantin A. Rybnikov
CCCG
2006
13 years 11 months ago
Spanning trees across axis-parallel segments
Abstract. Given a set P of points and a set S of pairwise disjoint axis-parallel line segments in the plane, we construct a straight line spanning tree T on P such that every segme...
Csaba D. Tóth, Michael Hoffmann