Abstract
Given a text T of length n, the sparse suffix sorting problem asks for the lexicographic order of suffixes starting at m selectable text positions P. The suffix binary search tree [Irving and Love, JDA’03] is a dynamic data structure that can answer this problem dynamically in the sense that insertions and deletions of positions in P are allowed. While a standard binary search tree on strings needs to store two longest-common prefix (LCP) values per node for providing the same query bounds, each suffix binary search tree node only stores a single LCP value and a bit flag. Its tree topology induces the sorting of the m suffixes by an Euler tour in \({{\mathcal {O}}}(m)\) time. However, it has not been addressed how to compute the lengths of the longest common prefixes of two suffixes with neighboring ranks with this data structure. We show that we can compute these lengths again by an Euler tour in \({{\mathcal {O}}}(m)\) time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Adelson-Velsky, G.M., Landis, E.M.: An algorithm for organization of information. Dokl. Akad. Nauk SSSR 146, 263–266 (1962)
Bille, P., Fischer, J., Gørtz, I.L., Kopelowitz, T., Sach, B., Vildhøj, H.W.: Sparse text indexing in small space. ACM Trans. Algorithms 12(3), 39:1–39:19 (2016)
Birenzwige, O., Golan, S., Porat, E.: Locally consistent parsing for text indexing in small space. In: Proceedings of SODA, pp. 607–626 (2020)
Burrows, M., Wheeler, D.J.: A block sorting lossless data compression algorithm. Technical report 124, Digital Equipment Corporation, Palo Alto, California (1994)
Chien, Y., Hon, W., Shah, R., Thankachan, S.V., Vitter, J.S.: Geometric BWT: compressed text indexing via sparse suffixes and range searching. Algorithmica 71(2), 258–278 (2015)
Ferragina, P., Fischer, J.: Suffix arrays on words. In: Ma, B., Zhang, K. (eds.) CPM 2007. LNCS, vol. 4580, pp. 328–339. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73437-6_33
Fischer, J., I, T., Köppl, D.: Deterministic sparse suffix sorting in the restore model. ACM Trans. Algorithms 16(4), 50:1–50:53 (2020)
I, T., Kärkkäinen, J., Kempa, D.: Faster sparse suffix sorting. In: Proceedings of STACS. LIPIcs, vol. 25, pp. 386–396 (2014)
I, T., Köppl, D.: Load-balancing succinct B trees. arXiv CoRR abs/2104.08751 (2021)
Irving, R.W., Love, L.: Suffix binary search trees and suffix arrays. University of Glasgow, Technical report (2001)
Irving, R.W., Love, L.: The suffix binary search tree and suffix AVL tree. J. Discret. Algorithms 1(5–6), 387–408 (2003)
Kärkkäinen, J., Kempa, D.: LCP array construction using O(sort(n)) (or Less) I/Os. In: Inenaga, S., Sadakane, K., Sakai, T. (eds.) SPIRE 2016. LNCS, vol. 9954, pp. 204–217. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46049-9_20
Kärkkäinen, J., Ukkonen, E.: Sparse suffix trees. In: Cai, J.-Y., Wong, C.K. (eds.) COCOON 1996. LNCS, vol. 1090, pp. 219–230. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61332-3_155
Khan, Z., Bloom, J.S., Kruglyak, L., Singh, M.: A practical algorithm for finding maximal exact matches in large sequence datasets using sparse suffix arrays. Bioinform. 25(13), 1609–1616 (2009)
Kolpakov, R., Kucherov, G., Starikovskaya, T.A.: Pattern matching on sparse suffix trees. In: Proceedings of CCP, pp. 92–97 (2011)
Köppl, D.: Exploring regular structures in strings. Ph.D. thesis, TU Dortmund (2018)
Kosolobov, D., Sivukhin, N.: Construction of sparse suffix trees and LCE indexes in optimal time and space. arXiv CoRR abs/2105.03782 (2021)
Love, L.: The suffix binary search tree. Ph.D. thesis, University of Glasgow, UK (2001)
Manber, U., Myers, E.W.: Suffix arrays: a new method for on-line string searches. SIAM J. Comput. 22(5), 935–948 (1993)
Prezza, N.: In-place sparse suffix sorting. In: Proceedings of SODA, pp. 1496–1508 (2018)
Uemura, T., Arimura, H.: Sparse and truncated suffix trees on variable-length codes. In: Giancarlo, R., Manzini, G. (eds.) CPM 2011. LNCS, vol. 6661, pp. 246–260. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21458-5_22
Vyverman, M., Baets, B.D., Fack, V., Dawyndt, P.: essaMEM: finding maximal exact matches using enhanced sparse suffix arrays. Bioinform. 29(6), 802–804 (2013)
Acknowledgments
This work was supported by JSPS KAKENHI Grant Numbers JP21K17701 (DK) and JP19K20213 (TI). We thank the four anonymous reviewers of SPIRE’21 for their valuable comments on our manuscript. They give additional inspiration for Corollary 1 and proposed the problem of how to efficiently merge two suffix binary search tree instances. Tackling this problem could indeed be useful for building and updating FM-indexes and other related indexing data structures.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
I, T., Irving, R.W., Köppl, D., Love, L. (2021). Extracting the Sparse Longest Common Prefix Array from the Suffix Binary Search Tree. In: Lecroq, T., Touzet, H. (eds) String Processing and Information Retrieval. SPIRE 2021. Lecture Notes in Computer Science(), vol 12944. Springer, Cham. https://doi.org/10.1007/978-3-030-86692-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-86692-1_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-86691-4
Online ISBN: 978-3-030-86692-1
eBook Packages: Computer ScienceComputer Science (R0)