On the cost of interchange rearrangement in strings

  • Authors:

  • Amihood Amir;Tzvika Hartman;Oren Kapah;Avivit Levy;Ely Porat

  • Affiliations:

  • Department of Computer Science, Bar Ilan University, Ramat Gan, Israel and Department of Computer Science, Johns Hopkins University, Baltimore, MD;Department of Computer Science, Bar Ilan University, Ramat Gan, Israel;Department of Computer Science, Bar Ilan University, Ramat Gan, Israel;Department of Computer Science, Bar Ilan University, Ramat Gan, Israel;Department of Computer Science, Bar Ilan University, Ramat Gan, Israel

  • Venue:
  • ESA'07 Proceedings of the 15th annual European conference on Algorithms
  • Year:
  • 2007

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Abstract

An underlying assumption in the classical sorting problem is that the sorter does not know the index of every element in the sorted array. Thus, comparisons are used to determine the order of elements, while the sorting is done by interchanging elements. In the closely related interchange rearrangement problem, final positions of elements are already given, and the cost of the rearrangement is the cost of the interchanges. This problem was studied only for the limited case of permutation strings, where every element appears once. This paper studies a generalization of the classical and well-studied problem on permutations by considering general strings input, thus solving an open problem of Cayley from 1849, and examining various cost models.