41,894 research outputs found
Skeletal Rigidity of Phylogenetic Trees
Motivated by geometric origami and the straight skeleton construction, we
outline a map between spaces of phylogenetic trees and spaces of planar
polygons. The limitations of this map is studied through explicit examples,
culminating in proving a structural rigidity result.Comment: 17 pages, 12 figure
A Characterization of Visibility Graphs for Pseudo-Polygons
In this paper, we give a characterization of the visibility graphs of
pseudo-polygons. We first identify some key combinatorial properties of
pseudo-polygons, and we then give a set of five necessary conditions based off
our identified properties. We then prove that these necessary conditions are
also sufficient via a reduction to a characterization of vertex-edge visibility
graphs given by O'Rourke and Streinu
Covering the Boundary of a Simple Polygon with Geodesic Unit Disks
We consider the problem of covering the boundary of a simple polygon on n
vertices using the minimum number of geodesic unit disks. We present an O(n
\log^2 n+k) time 2-approximation algorithm for finding the centers of the
disks, with k denoting the number centers found by the algorithm
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