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CATS
2007
14 years 28 days ago
Computing a Minimum-Dilation Spanning Tree is NP-hard
Given a set S of n points in the plane, a minimumdilation spanning tree of S is a tree with vertex set S of smallest possible dilation. We show that given a set S of n points and ...
Otfried Cheong, Herman J. Haverkort, Mira Lee
ISAAC
2003
Springer
96views Algorithms» more  ISAAC 2003»
14 years 4 months ago
On the Geometric Dilation of Finite Point Sets
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...
Annette Ebbers-Baumann, Ansgar Grüne, Rolf Kl...
ISAAC
2007
Springer
93views Algorithms» more  ISAAC 2007»
14 years 5 months ago
Dilation-Optimal Edge Deletion in Polygonal Cycles
Abstract. Let C be a polygonal cycle on n vertices in the plane. A randomized algorithm is presented which computes in O(n log3 n) expected time, the edge of C whose removal result...
Hee-Kap Ahn, Mohammad Farshi, Christian Knauer, Mi...