On shortest paths in polyhedral spaces
SIAM Journal on Computing
SIAM Journal on Computing
The number of shortest paths on the surface of a polyhedron
SIAM Journal on Computing
Shortest monotone descent path problem in polyhedral terrain
Computational Geometry: Theory and Applications
An Optimal-Time Algorithm for Shortest Paths on a Convex Polytope in Three Dimensions
Discrete & Computational Geometry
Shortest descending paths through given faces
Computational Geometry: Theory and Applications
Approximation algorithms for shortest descending paths in terrains
Journal of Discrete Algorithms
On the number of shortest descending paths on the surface of a convex terrain
Journal of Discrete Algorithms
An improved algorithm for the shortest descending path on a convex terrain
Journal of Discrete Algorithms
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We study the problem of finding a shortest descending path (SDP) between a pair of points, called source (s) and destination (t), on the surface of a triangulated convex terrain with n faces. A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. Time and space complexity requirement of our algorithm are O(@m(n)logn) and O(@t(n)), respectively. Here @m(n) and @t(n) are time and space complexity requirement for finding shortest geodesic path (SGP) between a pair of points on the surface of a convex polyhedra. The best known bounds on @m(n) and @t(n) are both O(nlogn) due to Schreiber and Sharir (2008) [11]. Earlier best known time and space complexity results of SDP on convex terrain were O(n^2logn) and O(n^2), respectively, and appears in Roy et al. (2007) [10]. Thus our algorithm improves both time and space complexity requirement of SDP problem by almost a linear factor over earlier best known results.