SCG '87 Proceedings of the third annual symposium on Computational geometry
A new algorithm for computing shortest paths in weighted planar subdivisions (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximating weighted shortest paths on polyhedral surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximation algorithms for geometric shortest path problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
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
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
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In this paper we define piecewise pseudo-Euclidean optimal path problems, where each region has a distinct cost metric of a class we call pseudo-Euclidean, that allows the path cost to possibly vary within the region in a predictable and efficiently computable way. This pseudo-Euclidean class of costs allows us to model a wide variety of various geographical features. We provide an approximation algorithm named BUSHWHACK that efficiently solves these piecewise pseudo-Euclidean optimal path problems. BUSHWHACK uses a previously known technique of dynamically generating a discretization in progress. However, it combines with this technique a "lazy" and best-first path propagation scheme so that fewer edges need to be added into the discretization. We show both analytically and experimentally that BUSHWHACK is more efficient than approximation algorithms based on Dijkstra's algorithm.