Abstract
A transposition is an operation that exchanges two adjacent substrings. When it is restricted so that one of the substrings is a prefix, it is called a prefix transposition. The prefix transposition distance between a pair of strings (permutations) is the shortest sequence of prefix transpositions required to transform a given string (permutation) into another given string (permutation). This problem is a variation of the transposition distance problem, related to genome rearrangements. An upper bound of n-1 and a lower bound of n/2 are known. We improve the bounds to n-log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> n and 2n/3 respectively. We also give upper and lower bounds for the prefix transposition distance on strings. For example, n/2 prefix transpositions are always sufficient for binary strings. We also prove that the exact prefix transposition distance problem on strings is NP complete.
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