Geodesic
On an algorithm to decide whether a free group is a free factor of another
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 2, pp. 395-414

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We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F. We show that the latter dependency can be made exponential in the rank difference rank(F) - rank(H), which often makes a significant change.

DOI : 10.1051/ita:2007040
Classification : 20E05, 05C25
Keywords: combinatorial group theory, free groups, free factors, inverse automata, algorithms 
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     author = {Silva, Pedro V. and Weil, Pascal},
     title = {On an algorithm to decide whether a free group is a free factor of another},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {395--414},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {2},
     year = {2008},
     doi = {10.1051/ita:2007040},
     mrnumber = {2401269},
     zbl = {1146.20021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2007040/}
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Silva, Pedro V.; Weil, Pascal. On an algorithm to decide whether a free group is a free factor of another. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 2, pp. 395-414. doi: 10.1051/ita:2007040

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