Shortest Gently Descending Paths

Authors:
Mustaq Ahmed;Anna Lubiw;Anil Maheshwari
Affiliations:
D. R. C. School of Computer Science, University of Waterloo, Canada;D. R. C. School of Computer Science, University of Waterloo, Canada;School of Computer Science, Carleton University, Canada
Venue:
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Year:
2009

Citing 10
Cited 0

The weighted region problem: finding shortest paths through a weighted planar subdivision

Journal of the ACM (JACM)
Shortest Anisotropic Paths on Terrains

ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Determining approximate shortest paths on weighted polyhedral surfaces

Journal of the ACM (JACM)
Shortest monotone descent path problem in polyhedral terrain

Computational Geometry: Theory and Applications
Approximate shortest paths in anisotropic regions

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Shortest descending paths through given faces

Computational Geometry: Theory and Applications
BUSHWHACK: An Approximation Algorithm for Minimal Paths through Pseudo-Euclidean Spaces

ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
On discretization methods for approximating optimal paths in regions with direction-dependent costs

Information Processing Letters
On finding approximate optimal paths in weighted regions

Journal of Algorithms
On finding energy-minimizing paths on terrains

IEEE Transactions on Robotics

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 . We introduce a generalization of the shortest descending path problem, called the shortest gently descending path (SGDP) problem, where a path descends, but not too steeply. The additional constraint to disallow a very steep descent makes the paths more realistic in practice. We give two approximation algorithms (more precisely, FPTASs) to solve the SGDP problem on general terrains.