Abstract
Given an input string S and a target string T when S is a permutation of T, the interchange rearrangement problem is to apply on S a sequence of interchanges, such that S is transformed into T. The interchange operation exchanges the position of the two elements on which it is applied. The goal is to transform S into T at the minimum cost possible, referred to as the distance between S and T. The distance can be defined by several cost models that determine the cost of every operation. There are two known models: The Unit-cost model and the Length-cost model. In this paper, we suggest a natural cost model: The Element-cost model. In this model, the cost of an operation is determined by the elements that participate in it. Though this model has been studied in other fields, it has never been considered in the context of rearrangement problems. We consider both the special case where all elements in S and T are distinct, referred to as a permutation string, and the general case, referred to as a general string. An efficient optimal algorithm for the permutation string case and efficient approximation algorithms for the general string case, which is \(\cal{NP}\)-hard, are presented.
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References
Amir, A., Aumann, Y., Benson, G., Levy, A., Lipsky, O., Porat, E., Skiena, S., Vishne, U.: Pattern matching with address errors: Rearrangement distances. In: Proc. of the 17th annual ACM-SIAM Symposium on Discrete Algorithm (SODA), pp. 1221–1229 (2006)
Amir, A., Aumann, Y., Indyk, P., Levy, A., Porat, E.: Efficient computations of ℓ1 and ℓ ∞ . In: Ziviani, N., Baeza-Yates, R. (eds.) SPIRE 2007. LNCS, vol. 4726, pp. 39–49. Springer, Heidelberg (2007)
Amir, A., Aumann, Y., Kapah, O., Levy, A., Porat, E.: Approximate string matching with address bit errors. In: Proc. of the 19th Annual Symposium on Combinatorial Pattern Matching (CPM), pp. 118–130 (2008)
Amir, A., Hartman, T., Kapah, O., Levy, A., Porat, E.: On the cost of interchange rearrangement in strings. In: Arge, L., Hoffmann, M., Welzl, E. (eds.) ESA 2007. LNCS, vol. 4698, pp. 99–110. Springer, Heidelberg (2007)
Angelov, S., Kunal, K., McGregor, A.: Sorting and selection with random costs. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds.) LATIN 2008. LNCS, vol. 4957, pp. 48–59. Springer, Heidelberg (2008)
Bafna, V., Pevzner, P.A.: Sorting by transpositions. SIAM Journal on Discrete Mathematics 11, 224–240 (1998)
Bender, M.A., Ge, D., He, S., Hu, H., Pinter, R.Y., Skiena, S., Swidan, F.: Improved bounds on sorting with length-weighted reversals. In: Proc. of the 15th annual ACM-SIAM Symposium on Discrete Algorithm (SODA), pp. 919–928 (2004)
Berman, P., Hannenhalli, S.: Fast sorting by reversal. In: Proc. 8th Annual Symposium on Combinatorial Pattern Matching (CPM), vol. 1075, pp. 168–185 (1996)
Carpara, A.: Sorting by reversals is difficult. In: Proc. 1st Annual Intl. Conf. on Research in Computational Biology (RECOMB), pp. 75–83 (1997)
Cayley, A.: Note on the theory of permutations. Philosophical Magazine 34, 527–529 (1849)
Christie, D.A.: Sorting by block-interchanges. Information Processing Letters 60, 165–169 (1996)
Gupta, A., Kumar, A.: Sorting and selection with structured costs. In: Proc. of the 42nd Symposium on Foundations of Computer Science (FOCS), pp. 416–425 (2001)
Gusfield, D.: Algorithms on strings, trees, and sequences: Computer science and computational biology. Cambridge University Press, Cambridge (1997)
Heath, L.S., Vergara, J.P.C.: Sorting by bounded block-moves. Discrete Applied Mathematics 88(1-3), 181–206 (1998)
Heath, L.S., Vergara, J.P.C.: Sorting by short swaps. Journal of Computational Biology 10(5), 775–789 (2003)
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Kapah, O., Landau, G.M., Levy, A., Oz, N. (2008). Interchange Rearrangement: The Element-Cost Model. In: Amir, A., Turpin, A., Moffat, A. (eds) String Processing and Information Retrieval. SPIRE 2008. Lecture Notes in Computer Science, vol 5280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89097-3_22
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DOI: https://doi.org/10.1007/978-3-540-89097-3_22
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