Abstract
An edit distance is a metric between words that quantifies how two words differ by counting the number of edit operations needed to transform one word into the other one. A word f is said isometric with respect to an edit distance if, for any pair of f-free words u and v, there exists a transformation of minimal length from u to v via the related edit operations such that all the intermediate words are also f-free. The adjective “isometric” comes from the fact that, if the Hamming distance is considered (i.e., only mismatches), then isometric words define some isometric subgraphs of hypercubes. We consider the case of edit distance with swap and mismatch. We compare it with the case of mismatch only and prove some properties of isometric words that are related to particular features of their overlaps.
Partially supported by INdAM-GNCS Project 2022 and 2023, FARB Project ORSA229894 of University of Salerno, TEAMS Project and PNRR MUR Project PE0000013-FAIR University of Catania, PNRR MUR Project ITSERR CUP B53C22001770006 and FFR fund University of Palermo, MUR Excellence Department Project MatMod@TOV, CUP E83C23000330006, awarded to the Department of Mathematics, University of Rome Tor Vergata.
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References
Amir, A., Cole, R., Hariharan, R., Lewenstein, M., Porat, E.: Overlap matching. Inf. Comput. 181(1), 57–74 (2003)
Amir, A., Eisenberg, E., Porat, E.: Swap and mismatch edit distance. Algorithmica 45(1), 109–120 (2006)
Anselmo, M., Flores, M., Madonia, M.: Quaternary n-cubes and isometric words. In: Lecroq, T., Puzynina, S. (eds.) WORDS 2021. LNCS, vol. 12847, pp. 27–39. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-85088-3_3
Anselmo, M., Flores, M., Madonia, M.: Fun slot machines and transformations of words avoiding factors. In: 11th International Conference on Fun with Algorithms. LIPIcs, vol. 226, pp. 4:1–4:15 (2022)
Anselmo, M., Flores, M., Madonia, M.: On k-ary n-cubes and isometric words. Theor. Comput. Sci. 938, 50–64 (2022)
Anselmo, M., Giammarresi, D., Madonia, M., Selmi, C.: Bad pictures: some structural properties related to overlaps. In: Jirásková, G., Pighizzini, G. (eds.) DCFS 2020. LNCS, vol. 12442, pp. 13–25. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-62536-8_2
Béal, M., Crochemore, M.: Checking whether a word is Hamming-isometric in linear time. Theor. Comput. Sci. 933, 55–59 (2022)
Béal, M.-P., Mignosi, F., Restivo, A.: Minimal forbidden words and symbolic dynamics. In: Puech, C., Reischuk, R. (eds.) STACS 1996. LNCS, vol. 1046, pp. 555–566. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-60922-9_45
Castiglione, G., Mantaci, S., Restivo, A.: Some investigations on similarity measures based on absent words. Fundam. Informaticae 171(1–4), 97–112 (2020)
Charalampopoulos, P., Crochemore, M., Fici, G., Mercas, R., Pissis, S.P.: Alignment-free sequence comparison using absent words. Inf. Comput. 262, 57–68 (2018)
Dombb, Y., Lipsky, O., Porat, B., Porat, E., Tsur, A.: The approximate swap and mismatch edit distance. Theor. Comput. Sci. 411(43), 3814–3822 (2010)
Faro, S., Pavone, A.: An efficient skip-search approach to swap matching. Comput. J. 61(9), 1351–1360 (2018)
Galil, Z., Park, K.: An improved algorithm for approximate string matching. SIAM J. Comput. 19, 989–999 (1990)
Hsu, W.J.: Fibonacci cubes-a new interconnection topology. IEEE Trans. Parallel Distrib. Syst. 4(1), 3–12 (1993)
Ilić, A., Klavžar, S., Rho, Y.: The index of a binary word. Theor. Comput. Sci. 452, 100–106 (2012)
Klavžar, S., Shpectorov, S.V.: Asymptotic number of isometric generalized Fibonacci cubes. Eur. J. Comb. 33(2), 220–226 (2012)
Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. Cybern. Control Theory 10, 707–710 (1966)
Wagner, R.A.: On the complexity of the extended string-to-string correction problem. In: Rounds, W.C., Martin, N., Carlyle, J.W., Harrison, M.A. (eds.) Proceedings of the 7th Annual ACM Symposium on Theory of Computing, 5–7 May 1975, Albuquerque, New Mexico, USA, pp. 218–223 (1975)
Wei, J.: The structures of bad words. Eur. J. Comb. 59, 204–214 (2017)
Wei, J., Yang, Y., Zhu, X.: A characterization of non-isometric binary words. Eur. J. Comb. 78, 121–133 (2019)
Wei, J., Zhang, H.: Proofs of two conjectures on generalized Fibonacci cubes. Eur. J. Comb. 51, 419–432 (2016)
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Anselmo, M., Castiglione, G., Flores, M., Giammarresi, D., Madonia, M., Mantaci, S. (2023). Isometric Words Based on Swap and Mismatch Distance. In: Drewes, F., Volkov, M. (eds) Developments in Language Theory. DLT 2023. Lecture Notes in Computer Science, vol 13911. Springer, Cham. https://doi.org/10.1007/978-3-031-33264-7_3
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