Proceedings  31st Annual Symposium on Foundations of Computer Science (1990)
St. Louis, MO, USA
Oct. 22, 1990 to Oct. 24, 1990
pp: 857-865 vol.2
L. Babai , Chicago Univ., IL, USA
The diameter of a group G with respect to a set S of generators is the maximum over g in G of the length of the shortest word in S union S/sup -1/ representing g. This concept arises in the contexts of efficient communication networks and Rubik's-cube-type puzzles. 'Best' generators are pertinent to networks, whereas 'worst' and 'average' generators seem more adequate models for puzzles. A substantial body of recent work on these subjects by the authors is surveyed. Regarding the 'best' case, it is shown that, although the structure of the group is essentially irrelevant if mod S mod is allowed to exceed (log mod G mod )/sup 1+c/(c>0), it plays a strong role when mod S mod =O(1).
Rubik's-cube, finite groups, generators, communication networks
L. Babai, A. Seress, A. Lubotzky, G. Hetyei and W. Kantor, "On the diameter of finite groups," Proceedings  31st Annual Symposium on Foundations of Computer Science(FOCS), St. Louis, MO, USA, 1990, pp. 857-865 vol.2.