Heuristics for the whitehead minimization problem

R. M. Haralick, A. D. Miasnikov, A. G. Myasnikov

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper we discuss several heuristic strategies which allow one to solve the Whitehead minimization problem much faster (on most inputs) than the classical Whitehead algorithm. The mere fact that these strategies work in practice leads to several interesting mathematical conjectures. In particular, we conjecture that the length of most nonminimal elements in a free group can be reduced by a Nielsen automorphism which can be identified by inspecting the structure of the corresponding Whitehead graph.

Original languageEnglish
Pages (from-to)7-14
Number of pages8
JournalExperimental Mathematics
Volume14
Issue number1
DOIs
StatePublished - 2005

Keywords

  • Automorphisms of a free group
  • Clustering
  • Search heuristics
  • Statistical group theory
  • Whitehead method

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