Shortest path queries in rectilinear worlds of higher dimension (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Shortest Path Problems on a Polyhedral Surface
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
The geodesic diameter of polygonal domains
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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We present an &Ogr;(n14 log n) algorithm for computing the geodesic diameter of a 3-polytope of n vertices. The geodesic diameter is the greatest separation between two points on the surface, where distance is determined by the shortest (geodesic) path between two points. We assume a model of computation that permits finding roots of a one-variable polynomial of fixed degree in constant time. The key geometric result underlying the algorithm is that, although it may be that neither endpoint of the diameter is a vertex of the polytope, when this occurs, there must be at least five distinct equal-length paths between the diameter endpoints.