Shortest Path Problems on a Polyhedral Surface

Atlas F. Cook, Carola Wenk
2012 Algorithmica  
We develop algorithms to compute edge sequences, Voronoi diagrams, shortest path maps, the Fréchet distance, and the diameter for a polyhedral surface. Distances on the surface are measured either by the length of a Euclidean shortest path or by link distance. Corollary 4. The link diameter of N can be computed in O(M 19 3 log 3.11 M ) time and O(M 3 ) space. Proof. Partition each of the O(M ) edges of N into O(M 3 ) edgelets with Lemma 3. Choose a point s in each of these O(M 4 ) edgelets. For
more » ... each of these points, construct the O(M 2 ) possible (v, e) edges of SPM(s, N ) without computing the arrangement of these edges. This can be done in O(M 7 3 log 3.11 M ) time per edgelet
doi:10.1007/s00453-012-9723-6 fatcat:ebu7n3elgbertijtsoh7mwoipa