Whitehead method and Genetic Algorithms

Details Whitehead method and Genetic Algorithms Whitehead method and Genetic Algorithms

2003-04-20

arxiv.org/abs/math/0304283v1

Mathematics

Group Theory

29 pages, 7 figures

Scientific paper

In this paper we discuss a genetic version (GWA) of the Whitehead's algorithm, which is one of the basic algorithms in combinatorial group theory. It turns out that GWA is surprisingly fast and outperforms the standard Whitehead's algorithm in free groups of rank >= 5. Experimenting with GWA we collected an interesting numerical data that clarifies the time-complexity of the Whitehead's Problem in general. These experiments led us to several mathematical conjectures. If confirmed they will shed light on hidden mechanisms of Whitehead Method and geometry of automorphic orbits in free groups.

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