Geometric Dilation of Closed Planar Curves: New (2008)
Lower Bounds, Annette Ebbers-baumann, Ansgar Grüne, Rolf Klein
Given two points on a closed planar curve, C, we can divide the length of a shortest connecting path in C by their Euclidean distance. The supremum of these ratios, taken over all pairs of points on...
The Geometric Dilation of Finite Point Sets (2006)
Annette Ebbers-Baumann, Ansgar Grüne, Rolf Klein
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 Euclidean distance. The...
Geometric Dilation of Closed Planar Curves: New Lower Bounds (2006)
Lower Bounds, Annette Ebbers-Baumann, Ansgar Grüne, Rolf Klein
Given two points on a closed planar curve, C, we can divide the length of a shortest connecting path in C by their Euclidean distance. The supremum of these ratios, taken over all pairs of points on...
Annette Ebbers-baumann, Ansgar Grüne, Rolf Klein, Marek Karpinski, Christian Knauer, A. Ebbers-baumann, ...
Let S be a set of points in the plane. What is the minimum possible dilation of all plane graphs that contain S? Even for a set S as simple as five points evenly placed on the circle, this question...
Annette Ebbers-baumann, Ansgar Grüne, Rolf Klein, Marek Karpinski, Christian Knauer
Communicated by Li Zhang Let S be a set of points in the plane. What is the minimum possible dilation of all plane graphs that contain S? Even for a set S as simple as five points evenly placed on...
On Geometric Dilation and Halving Chords (2005)
Adrian Dumitrescu, Annette Ebbers-Baumann, Ansgar Grüne, Rolf Klein, Günter Rote
Let G be an embedded planar graph whose edges may be curves. The detour between two points, p and q (on edges or vertices) of G, is the ratio between the shortest path in G between p and q and their...
Embedding Point Sets into Plane Graphs of Small Dilation (2005)
Annette Ebbers-Baumann, Ansgar Grüne, Marek Karpinski, Rolf Klein, Christian Knauer, Andrzej Lingas
Let S be a set of points in the plane. What is the minimum possible dilation of all plane graphs that contain S?EvenforasetS as simple as five points evenly placed on the circle, this question seems...
On the Geometric Dilation of Closed Curves, Graphs and Point Sets (2005)
Adrian Dumitrescu, Annette Ebbers-baumann, Ansgar Grüne, Rolf Klein, Günter Rote
Let G be an embedded planar graph whose edges are curves. The detour between two points p and q (on edges or vertices) of G is the ratio between the length of a shortest path connecting p and q in G...
On the Geometric Dilation of Closed Curves, Graphs and Point Sets (2005)
Adrian Dumitrescu, Annette Ebbers-baumann
Abstract Let G be an embedded planar graph whose edges are curves. The detour between two points p and q (on edges or vertices) of G is the ratio between the length of a shortest path connecting p...
On geometric dilation and halving chords (2005)
Adrian Dumitrescu, Annette Ebbers-baumann, Ansgar Grüne, Rolf Klein, Günter Rote
Abstract. Let G be an embedded planar graph whose edges may be curves. The detour between two points, p and q (on edges or vertices) of G, is the ratio between the shortest path in G between p and q...
Embedding point sets into plane graphs of small dilation (2005)
Annette Ebbers-baumann, Ansgar Grüne, Marek Karpinski, Rolf Klein, Christian Knauer, Andrzej Lingas
Let S be a set of points in the plane. What is the minimum possible dilation of all plane graphs that contain S? Even for a set S as simple as five points evenly placed on the circle, this question...
On the geometric dilation of closed curves, graphs, and point sets (2004)
Dumitrescu, Adrian, Ebbers-Baumann, Annette, Grüne, Ansgar, Klein, Rolf, Rote, Günter
The detour between two points u and v (on edges or vertices) of an embedded planar graph whose edges are curves is the ratio between the shortest path in in the graph between u and v and their...
On the Geometric Dilation of Finite Point Sets (2003)
Annette Ebbers-Baumann, Ansgar Grüne, Rolf Klein
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 Euclidean distance.