Geodesic
Finding Shortest Paths With Computational Geometry
Journal of Graph Algorithms and Applications, Tome 7 (2003) no. 3, pp. 287-303.

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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. 
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     author = {Po-Shen Loh},
     title = {Finding {Shortest} {Paths} {With} {Computational} {Geometry}},
     journal = {Journal of Graph Algorithms and Applications},
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     doi = {10.7155/jgaa.00071},
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Po-Shen Loh. Finding Shortest Paths With Computational Geometry. Journal of Graph Algorithms and Applications, Tome 7 (2003) no. 3, pp. 287-303. doi : 10.7155/jgaa.00071. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00071/

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