Finding Shortest Paths With Computational Geometry

We present a heuristic search algorithm for the R 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 n) time and O(n logd−1 n) space, where n is the number of visited vertices. We achieve this result by embedding the problem in R and identifying heuristic calculations as instances of a dynamic closest-point problem, to which we then apply methods from computational geometry. Communicated by Joseph S.B. Mitchell: submitted October 2002; revised June 2003. Research supported by Axline and Larson fellowships from the California Institute of Technology. Po-Shen Loh, Finding Shortest Paths, JGAA, 7(3) 287–303 (2003) 288