SCG '86 Proceedings of the second annual symposium on Computational geometry
On shortest paths in polyhedral spaces
SIAM Journal on Computing
Shortest path between two simple polygons
Information Processing Letters
SIAM Journal on Computing
Art gallery theorems and algorithms
Art gallery theorems and algorithms
SCG '87 Proceedings of the third annual symposium on Computational geometry
An algorithmic approach to some problems in terrain navigation
Artificial Intelligence - Special issue on geometric reasoning
On maximum flows in polyhedral domains
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Proximity and reachability in the plane.
Proximity and reachability in the plane.
On maximum flows in polyhedral domains
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Gross motion planning—a survey
ACM Computing Surveys (CSUR)
Shortest path queries among weighted obstacles in the rectilinear plane
Proceedings of the eleventh annual symposium on Computational geometry
Optimal Collision Free Path Planning for Non-Synchronized Motions
Journal of Intelligent and Robotic Systems
Link Distance and Shortest Path Problems in the Plane
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Link distance and shortest path problems in the plane
Computational Geometry: Theory and Applications
A survey of geodesic paths on 3D surfaces
Computational Geometry: Theory and Applications
| Hi-index | 0.00 |
We consider the terrain navigation problem in a two-dimensional polygonal subdivision consisting of obstacles, “free” regions (in which one can travel at no cost), and regions in which cost is proportional to distance traveled. This problem is a special case of the weighted region problem and is a generalization of the well-known planar shortest path problem in the presence of obstacles. We present an &Ogr;(n2) exact algorithm for this problem and faster algorithms for the cases of convex free regions and/or obstacles. We generalize our algorithm to allow arbitrary weights on the edges of the subdivision. In addition, we present algorithms to solve a variety of important applications: (1) an &Ogr;(n2W) algorithm for finding lexicographically shortest paths in weighted regions (with W different weights); (2) an &Ogr;(k2n2) algorithm for planning least-risk paths in a simple polygon that contains k line-of-sight threats (this becomes &Ogr;(k4n4) in polygons with holes); and (3) an &Ogr;(k2n3) algorithm for finding least-risk watchman routes in simple rectilinear polygons (a watchman route is such that each point in the polygon is visible from at least one point along the route).