# Lower Bounds for Shortest Path and Related ProblemsJohn

@inproceedings{Canny1987LowerBF, title={Lower Bounds for Shortest Path and Related ProblemsJohn}, author={J. Canny and J. Reif}, year={1987} }

We present the rst lower bounds for shortest path problems (including euclidean shortest path) in three dimensions, and for some constrained motion planning problems in two and three dimensions. Our proofs are based a technique called free path encoding and use homotopy equivalence classes of paths to encode state. We rst apply the method to the shortest path problem in three dimensions. The problem is to nd the shortest path under an L metric (e.g. a euclidean metric) between two points amid… CONTINUE READING

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