Finding Shortest Paths With Computational Geometry

Abstract

We present a heuristic search algorithm for the R^d Manhattan shortest path problem that achieves front-to-front bidirectionality in subquadratic time. In the study of bidirectional search algorithms, front-to-front heuristic computations were thought to be prohibitively expensive (at least quadratic time complexity); our algorithm runs in O(n log^d n) time and O(n log^d−1 n) space, where n is the number of visited vertices. We achieve this result by embedding the problem in R^d+1 and identifying heuristic calculations as instances of a dynamic closest-point problem, to which we then apply methods from computational geometry.