| W. H. Gates and C. H. Papadimitriou. Bounds for sorting by prex reversals. Discrete Mathematics, 27:47-57, 1979. |
....by considering the (smaller) set of all transformations that reverse a pre x of the permutation. The diameter of the space of N element permutations under this distance function remains an open question; however, Gates and Papadimitriou showed that it lies between 17 16 N and 5 3 N O(1) [12]. Finally, one obtains the transposition distance by considering the set of all transformations that splice out a contiguous block of genes and re insert it (in the same order) elsewhere in the sequence. The diameter problem for this distance function is also an open question; Bafna and ....
W. H. Gates and C. H. Papadimitriou. Bounds for sorting by prex reversals. Discrete Mathematics, 27:47-57, 1979.
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