Approximating shortest paths on a convex polytope in three dimensions
Journal of the ACM (JACM)
Constructing approximate shortest path maps in three dimensions
Proceedings of the fourteenth annual symposium on Computational geometry
Approximation algorithms for geometric shortest path problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Parallel implementation of geometric shortest path algorithms
Parallel Computing - Special issue: High performance computing with geographical data
An optimal-time algorithm for shortest paths on a convex polytope in three dimensions
Proceedings of the twenty-second annual symposium on Computational geometry
Shortest paths on realistic polyhedra
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Efficiently determining a locally exact shortest path on polyhedral surfaces
Computer-Aided Design
A multi-resolution surface distance model for k-NN query processing
The VLDB Journal — The International Journal on Very Large Data Bases
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
Expansion-Based algorithms for finding single pair shortest path on surface
W2GIS'04 Proceedings of the 4th international conference on Web and Wireless Geographical Information Systems
| Hi-index | 0.00 |
We present an approximation algorithm that, given the boundary P of a simple, nonconvex polyhedron in 3-d, and two points s and t on P, constructs a path on P between s and t whose length is at most 7*(1+x)*d(s,t), where d(s,t) is the length of the shortest path between s and t on P, and x 0 is an arbitararily small positive constant. The algorithm runs in O(n^{5/3} log^{5/3} n) time, where n is the number of vertices in P. We also present a slightly faster algorithm that runs in O(n^{8/5} log^{8/5} n) time and returns a path whose length is at most 15*(1+x)*d(s,t).