Abstract
We present an algorithm to convert a word of length $n$ in the standard generators of the solvable Baumslag–Solitar group $\operatorname{BS}(1,p)$ into a geodesic word, which runs in linear time and $O(n\log n)$ space on a random access machine.
Citation
Murray Elder. "A linear-time algorithm to compute geodesics in solvable Baumslag–Solitar groups." Illinois J. Math. 54 (1) 109 - 128, Spring 2010. https://doi.org/10.1215/ijm/1299679740
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