Abstract
In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, can be considered as a relevant evolutionary distance. The problem of computing this distance when genomes are represented by permutations, called the Sorting by Transpositions problem (SBT), has been introduced by Bafna and Pevzner [3] in 1995. It has naturally been the focus of a number of studies, but the computational complexity of this problem has remained undetermined for 15 years.
In this paper, we answer this long-standing open question by proving that the Sorting by Transpositions problem is NP-hard. As a corollary of our result, we also prove that the following problem from [10] is NP-hard: given a permutation π, is it possible to sort π using d b (π)/3 permutations, where d b (π) is the number of breakpoints of π?
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Bulteau, L., Fertin, G., Rusu, I. (2011). Sorting by Transpositions Is Difficult. In: Aceto, L., Henzinger, M., Sgall, J. (eds) Automata, Languages and Programming. ICALP 2011. Lecture Notes in Computer Science, vol 6755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22006-7_55
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DOI: https://doi.org/10.1007/978-3-642-22006-7_55
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