The weighted region problem: finding shortest paths through a weighted planar subdivision
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
Determining approximate shortest paths on weighted polyhedral surfaces
Journal of the ACM (JACM)
On finding approximate optimal paths in weighted regions
Journal of Algorithms
On finding energy-minimizing paths on terrains
IEEE Transactions on Robotics
Approximation algorithms for shortest descending paths in terrains
Journal of Discrete Algorithms
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The optimal path planning problems are very difficult in the case where the cost metric varies not only in different regions of the space, but also in different directions inside the same region. If the classic discretization approach is adopted to compute an ε-approximation of the optimal path, the size of the discretization (and thus the complexity of the approximation algorithm) is usually dictated by a number of geometric parameters and thus can be very large. In this paper we show a general method for choosing the variables of the discretization to maximally reduce the dependency of the size of the discretization on various geometric parameters. We use this method to improve the previously reported results on two optimal path problems with direction-dependent cost metrics.