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Finding Shortest Paths With Computational Geometry

Loh, Po-Shen (2003) Finding Shortest Paths With Computational Geometry. Journal of Graph Algorithms and Applications, 7 (3). pp. 287-303. ISSN 1526-1719. http://resolver.caltech.edu/CaltechAUTHORS:LOHjgaa03

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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.


Item Type:Article
Additional Information: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. Special thanks to Alain Martin and Mika Nystr¨om for introducing this problem to the author, and to Charles Leiserson for providing pointers toward related literature. Thanks also to Po-Ru Loh for providing many valuable suggestions that significantly improved the clarity of this paper.
Record Number:CaltechAUTHORS:LOHjgaa03
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:LOHjgaa03
Alternative URL:http://jgaa.info/accepted/2003/Loh2003.7.3.pdf
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:756
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:27 Sep 2005
Last Modified:26 Dec 2012 08:41

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