Abstract
In this paper we combine two string searching related problems: the approximate string matching under parameters \(\delta \) and \(\gamma \), and the order preserving matching problem. Order-preserving matching regards the internal structure of the strings rather than their absolute values while matching under \(\delta \) and \(\gamma \) distances permit a level of error. We formally define the \(\delta \gamma \)–order-preserving matching problem. We designed two algorithms for it based on the segment tree and the Fenwick tree, respectively. Also, we design and implement in C++ and an experimental setup to compare these algorithms with the naive solution and the updateBA algorithm introduced in [22]. The data structure based algorithms show better experimental performance due to their better lower bound of \(\varOmega (n \lg n)\) complexity.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
de Berg, M., Cheong, O., van Kreveld, M., Overmars, M.: More Geometric Data Structures, pp. 219–241. Springer, Heidelberg (2008)
Brass, P.: Advanced Data Structures. Cambridge University Press, Cambridge (2008). Cambridge books online
Cambouropoulos, E., Crochemore, M., Iliopoulos, C., Mouchard, L., Pinzon, Y.: Algorithms for computing approximate repetitions in musical sequences. Int. J. Comput. Math. 79(11), 1135–1148 (2002)
Chhabra, T., Kulekci, M.O., Tarhio, J.: Alternative algorithms for order-preserving matching. In: Holub, J., Žďárek, J. (eds.) Proceedings of the Prague Stringology Conference 2015, pp. 36–46. Czech Technical University in Prague, Prague, Czech Republic (2015)
Chhabra, T., Tarhio, J.: Order-preserving matching with filtration. In: Gudmundsson, J., Katajainen, J. (eds.) SEA 2014. LNCS, vol. 8504, pp. 307–314. Springer, Cham (2014). doi:10.1007/978-3-319-07959-2_26
Crawford, T., Iliopoulos, C.S., Raman, R.: String-matching techniques for musical similarity and melodic recognition. Comput. Musicol. 11, 71–100 (1998)
Crochemore, M., Iliopoulos, C.S., Kociumaka, T., Kubica, M., Langiu, A., Pissis, S.P., Radoszewski, J., Rytter, W., Waleń, T.: Order-Preserving Incomplete Suffix Trees and Order-Preserving Indexes, pp. 84–95. Springer, Cham (2013)
Crochemore, M., Iliopoulos, C.S., Kociumaka, T., Kubica, M., Langiu, A., Pissis, S.P., Radoszewski, J., Rytter, W., Walen, T.: Order-preserving suffix trees and their algorithmic applications. CoRR abs/1303.6872 (2013)
Crochemore, M., Iliopoulos, C.S., Kociumaka, T., Kubica, M., Langiu, A., Pissis, S.P., Radoszewski, J., Rytter, W., Waleń, T.: Order-preserving indexing. Theor. Comput. Sci. 638(C), 122–135 (2016)
Faro, S., Külekci, M.O.: Efficient algorithms for the order preserving pattern matching problem. CoRR abs/1501.04001 (2015)
Fenwick, P.M.: A new data structure for cumulative frequency tables. Softw. Pract. Exp. 24, 327–336 (1994)
Gawrychowski, P., Uznański, P.: Order-preserving pattern matching with k mismatches. Theor. Comput. Sci. 638, 136–144 (2016)
Hasan, M.M., Islam, A., Rahman, M.S., Rahman, M.S.: Order Preserving Prefix Tables, pp. 111–116. Springer, Cham (2014)
Hasan, M.M., Islam, A., Rahman, M.S., Rahman, M.: Order preserving pattern matching revisited. Pattern Recogn. Lett. 55(C), 15–21 (2015)
Kim, J., Eades, P., Fleischer, R., Hong, S.H., Iliopoulos, C.S., Park, K., Puglisi, S.J., Tokuyama, T.: Order-preserving matching. Theor. Comput. Sci. 525, 68–79 (2014). Advances in Stringology
Kubica, M., Kulczyński, T., Radoszewski, J., Rytter, W.: WaleÅĎ, T.: A linear time algorithm for consecutive permutation pattern matching. Information Processing Letters 113(12), 430–433 (2013)
Lee, I., Mendivelso, J., Pinzón, Y.J.: \(\delta \gamma \)-Parameterized Matching, pp. 236–248. Springer, Heidelberg (2009)
Mendivelso, J.: Definition and solution of a new string searching variant termed \(\delta \gamma \)-parameterized matching. Master’s thesis, National University of Colombia, Bogota, Colombia (2010)
Mendivelso, J., Lee, I., Pinzón, Y.J.: Approximate Function Matching under \(\delta \)- and \(\gamma \)- Distances, pp. 348–359. Springer, Heidelberg (2012)
Mendivelso, J., Pino, C., Niño, L.F., Pinzón, Y.: Approximate Abelian Periods to Find Motifs in Biological Sequences, pp. 121–130. Springer, Cham (2015)
Mendivelso, J., Pinzón, Y.: A novel approach to approximate parikh matching for comparing composition in biological sequences. In: Proceedings of the 6th International Conference on Bioinformatics and Computational Biology (BICoB 2014) (2014)
Niquefa, R., Mendivelso, J., Hernández, G., Pinzón, Y.: Order preserving matching under \(\delta \gamma \)-approximation. In: Congreso Internacional de Ciencias Básicas e Ingeniería (2017)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Niquefa, R., Mendivelso, J., Hernández, G., Pinzón, Y. (2017). Segment and Fenwick Trees for Approximate Order Preserving Matching. In: Figueroa-García, J., López-Santana, E., Villa-Ramírez, J., Ferro-Escobar, R. (eds) Applied Computer Sciences in Engineering. WEA 2017. Communications in Computer and Information Science, vol 742. Springer, Cham. https://doi.org/10.1007/978-3-319-66963-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-66963-2_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66962-5
Online ISBN: 978-3-319-66963-2
eBook Packages: Computer ScienceComputer Science (R0)