Deterministic minimal time vessel routing
Operations Research
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
A new algorithm for computing shortest paths in weighted planar subdivisions (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
International Journal of Robotics Research
Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
An epsilon-Approximation for Weighted Shortest Paths on Polyhedral Surfaces
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
Movement Planning in the Presence of Flows
Algorithmica
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry — CCCG02
Geometric Spanner Networks
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Approximate Shortest Paths in Anisotropic Regions
SIAM Journal on Computing
Algorithms for Approximate Shortest Path Queries on Weighted Polyhedral Surfaces
Discrete & Computational Geometry
Approximate distance queries for weighted polyhedral surfaces
ESA'11 Proceedings of the 19th European conference on Algorithms
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We study the minimum cost path problem in an environment in which the cost is direction dependent (anisotropic). The problem arises in sailing, robotics, aircraft navigation, and routing of autonomous vehicles, where the cost is affected by the direction of waves, winds, or slope of the terrain. We present an approximation algorithm to find a minimum cost path for a point robot moving in a planar subdivision, in which each face is assigned a translational flow that reflects the cost of travelling within this face. Our main contribution is a data structure that, given a subdivision with translational flows, returns a (1+@e)-approximate minimum cost path in the subdivision between any two query points in the plane.