BUSHWHACK: An Approximation Algorithm for Minimal Paths through Pseudo-Euclidean Spaces

In this paper we deene 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 eeciently 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 eeciently 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-rst path propagation scheme so that fewer edges need to be added into the discretization. We show both analytically and experimentally that BUSHWHACK is more eecient than approximation algorithms based on Dijkstra's algorithm.