We present an efficient implementation of the solution to the conjugacy problem in Thompson's group F, a certain infinite group whose elements are piecewise-linear homeomorphisms of the unit interval. This algorithm checks for conjugacy by constructing and comparing directed graphs called strand diagrams. We provide a comprehensive description of our solution algorithm, including the data structure that stores strand diagrams and methods to simplify them. We prove that our algorithm theoretically achieves a linear time bound in the size of the input, and we present a quadratic time working solution. © 2013 IEEE.
Hossain, N., Mcgrail, R., Belk, J., Matucci, F. (2014). Deciding conjugacy in Thompson's group F in linear time. In Proceedings - 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2013 (pp.89-96). IEEE Computer Society [10.1109/SYNASC.2013.19].
Deciding conjugacy in Thompson's group F in linear time
Matucci, F
2014
Abstract
We present an efficient implementation of the solution to the conjugacy problem in Thompson's group F, a certain infinite group whose elements are piecewise-linear homeomorphisms of the unit interval. This algorithm checks for conjugacy by constructing and comparing directed graphs called strand diagrams. We provide a comprehensive description of our solution algorithm, including the data structure that stores strand diagrams and methods to simplify them. We prove that our algorithm theoretically achieves a linear time bound in the size of the input, and we present a quadratic time working solution. © 2013 IEEE.
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