Abstract
Transforming strings by exchanging elements at bounded distance is applicable in fields like molecular biology, pattern recognition and music theory. A reversal of length two at position i is denoted by (i i+1). When it is applied to π, where π = π 1,π 2, π 3,..., π i ,π i + 1, π n , it transforms π to π′, where π′ = π 1,π 2, π 3,..., π i − 1,π i + 1, π i , π i + 1, ..., π n . We call this operation an adjacent swap. We study the problem of computing the minimum number of adjacent swaps needed to transform one string of size n into another compatible string over an alphabet σ of size k, i.e. adjacent swap distance problem. O(nlog 2 n) time complexity algorithms are known for adjacent swap distance. We give an algorithm with O(nk) time for both signed and unsigned versions of this problem where k is the number of symbols. We also give an algorithm with O(nk) time for transforming signed strings with reversals of length up to 2, i.e. reversals of length 1 or 2.
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© 2008 Springer-Verlag Berlin Heidelberg
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Chitturi, B., Sudborough, H., Voit, W., Feng, X. (2008). Adjacent Swaps on Strings. In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_30
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DOI: https://doi.org/10.1007/978-3-540-69733-6_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69732-9
Online ISBN: 978-3-540-69733-6
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