Abstract
In this paper, we study local maximal antiperiodicities. Given a string X and an integer k, we compute the maximal k-antiperiodicity starting at every position of X; that is, we identify a maximum-length sequence of distinct factors, where each is of length k. The space and time complexity of the algorithm is linear.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alamro, H., Badkobeh, G., Belazzougui, D., Iliopoulos, C.S., Puglisi, S.J.: Computing the antiperiod (s) of a string. In: 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2019)
Alzamel, M., et al.: Online algorithms on antipowers and antiperiods. In: Brisaboa, N.R., Puglisi, S.J. (eds.) String Processing and Information Retrieval, pp. 175–188. Springer International Publishing, Cham (2019)
Badkobeh, G., Fici, G., Puglisi, S.J.: Algorithms for anti-powers in strings. Inf. Process. Lett. 137, 57–60 (2018)
Bannai, H., et al.: Diverse palindromic factorization is NP-complete. In: Potapov, I. (ed.) DLT 2015. LNCS, vol. 9168, pp. 85–96. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21500-6_6
Bulteau, L., et al.: Multivariate algorithmics for NP-hard string problems. Bulletin of EATCS 3(114) (2014)
Burcroff, A.: \((k,\lambda )\)-anti-powers and other patterns in words. Electron. J. Comb. 25(P4.41) (2018)
Condon, A., Maňuch, J., Thachuk, C.: Complexity of a collision-aware string partition problem and its relation to oligo design for gene synthesis. In: Hu, X., Wang, J. (eds.) COCOON 2008. LNCS, vol. 5092, pp. 265–275. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69733-6_27
Condon, A., Maňuch, J., Thachuk, C.: The complexity of string partitioning. J. Discrete Algorithms 32, 24–43 (2015)
Cox, J.C., Lape, J., Sayed, M.A., Hellinga, H.W.: Protein fabrication automation. Protein Sci. 16(3), 379–390 (2007)
Defant, C.: Anti-power prefixes of the Thue-Morse word. Electron. J. Comb. 24 (2017)
Farach, M.: Optimal suffix tree construction with large alphabets. In: Foundations of Computer Science, 1997. Proceedings., 38th Annual Symposium on, pp. 137–143. IEEE (1997)
Fici, G., Restivo, A., Silva, M., Zamboni, L.Q.: Anti-powers in infinite words. J. Comb. Theory, Ser. A 157, 109–119 (2018)
Gaetz, M.: Anti-power \( j \)-fixes of the thue-morse word. Discrete Math. Theoretical Comput. Sci. 23 (2021)
Kociumaka, T., Kubica, M., Radoszewski, J., Rytter, W., Waleń, T.: A linear time algorithm for seeds computation. In: Proceedings of the Twenty-third Annual ACM-SIAM Symposium on Discrete algorithms, pp. 1095–1112. SIAM (2012)
Kociumaka, T., Radoszewski, J., Rytter, W., Straszyński, J., Waleń, T., Zuba, W.: Efficient representation and counting of antipower factors in words. Inf. Comput. 286, 104779 (2022)
Stemmer, W.P., Crameri, A., Ha, K.D., Brennan, T.M., Heyneker, H.L.: Single-step assembly of a gene and entire plasmid from large numbers of oligodeoxyribonucleotides. Gene 164(1), 49–53 (1995)
Thue, A.: Uber unendliche zeichenreihen. Norske Vid Selsk. Skr. I Mat-Nat Kl. (Christiana) 7, 1–22 (1906)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 IFIP International Federation for Information Processing
About this paper
Cite this paper
Alzamel, M., Daykin, J.W., Hampson, C., Iliopoulos, C.S., Lim, Z., Smyth, W.F. (2023). Local Maximal Equality-Free Periodicities. In: Maglogiannis, I., Iliadis, L., Papaleonidas, A., Chochliouros, I. (eds) Artificial Intelligence Applications and Innovations. AIAI 2023 IFIP WG 12.5 International Workshops. AIAI 2023. IFIP Advances in Information and Communication Technology, vol 677. Springer, Cham. https://doi.org/10.1007/978-3-031-34171-7_29
Download citation
DOI: https://doi.org/10.1007/978-3-031-34171-7_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-34170-0
Online ISBN: 978-3-031-34171-7
eBook Packages: Computer ScienceComputer Science (R0)