Illinois Journal of Mathematics

A linear-time algorithm to compute geodesics in solvable Baumslag–Solitar groups

Murray Elder

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We present an algorithm to convert a word of length n in the standard generators of the solvable Baumslag–Solitar group BS(1, p) into a geodesic word, which runs in linear time and O(n log n) space on a random access machine.

Article information

Illinois J. Math. Volume 54, Number 1 (2010), 109-128.

First available in Project Euclid: 9 March 2011

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 68Q25: Analysis of algorithms and problem complexity [See also 68W40]


Elder, Murray. A linear-time algorithm to compute geodesics in solvable Baumslag–Solitar groups. Illinois Journal of Mathematics 54 (2010), no. 1, 109--128. doi:10.1214/10-AAP256.

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