Journal of Graph Algorithms and Applications
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Finding Shortest Paths With Computational Geometry
Vol. 7, no. 3, pp. 287-303, 2003. Regular paper.
Abstract We present a heuristic search algorithm for the Rd 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 logd 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 Rd+1 and identifying heuristic calculations as instances of a dynamic closest-point problem, to which we then apply methods from computational geometry.
Submitted: October 2002.
Revised: June 2003.
Communicated by Joseph S. B. Mitchell