TY - JOUR
T1 - Heuristics for the whitehead minimization problem
AU - Haralick, R. M.
AU - Miasnikov, A. D.
AU - Myasnikov, A. G.
PY - 2005
Y1 - 2005
N2 - 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.
AB - 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.
KW - Automorphisms of a free group
KW - Clustering
KW - Search heuristics
KW - Statistical group theory
KW - Whitehead method
UR - http://www.scopus.com/inward/record.url?scp=22544455976&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=22544455976&partnerID=8YFLogxK
U2 - 10.1080/10586458.2005.10128906
DO - 10.1080/10586458.2005.10128906
M3 - Article
AN - SCOPUS:22544455976
SN - 1058-6458
VL - 14
SP - 7
EP - 14
JO - Experimental Mathematics
JF - Experimental Mathematics
IS - 1
ER -