Summary: Discrete Mathematics 27 (1979) 47-57.
@ North-Holland Publishing Comp~ny
I' BOUNDS FOR SORTING BY PREFIX REVERSAL
William H. GATES
Christos H. PAP ADIMITRIOU*t
Departmentof ElectricalEngineering,Universityof California,Berkeley,CA 94720,U.S.A.
Microsoft, Albuquerque, New Mexico
Received 18danuary 1978
Revised 28 August 19(8
For a permutation (J"of the integers from 1 to n, let f((J")be the smallest number of prefix
reversalsthal'will transform (J"to the identity permutation, and let f(n) be the largest such f(lr)
for all (J"in (the symmetric group) Sn' We show that f(n) "'"(5n + 5)/3, and that f(n) ~ 17n/16 for
n a multiple of 16. if, furthermore, each integer is required to participate in an even number of
reversed prefixes, the corresponding function g(n) is shown to obey 3n/2-1""'g(n)""'2n+3.