Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
Approximation algorithms for geometric shortest path problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Computing the arrangement of curve segments: divide-and-conquer algorithms via sampling
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Determining approximate shortest paths on weighted polyhedral surfaces
Journal of the ACM (JACM)
Computing the Fréchet distance between simple polygons in polynomial time
Proceedings of the twenty-second annual symposium on Computational geometry
Querying approximate shortest paths in anisotropic regions
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Approximate shortest paths in anisotropic regions
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Walking your dog in the woods in polynomial time
Proceedings of the twenty-fourth annual symposium on Computational geometry
Exact algorithms for partial curve matching via the Fréchet distance
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On finding approximate optimal paths in weighted regions
Journal of Algorithms
Approximate shortest path queries on weighted polyhedral surfaces
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
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We discuss two versions of the Fréchet distance problem in weighted planar subdivisions. In the first one, the distance between two points is the weighted length of the line segment joining the points. In the second one, the distance between two points is the length of the shortest path between the points. In both cases we give algorithms for finding a (1 + 驴)-factor approximation of the Fréchet distance between two polygonal curves. We also consider the Fréchet distance between two polygonal curves among polyhedral obstacles in $\mathcal{R}^3$ (1/ 驴 weighted region problem) and present a (1 + 驴)-factor approximation algorithm.