Abstract
Cartesian tree matching is the problem of finding all substrings in a given text which have the same Cartesian trees as that of a given pattern. In this paper, we deal with Cartesian tree matching for the case of multiple patterns. We present two fingerprinting methods, i.e., the parent-distance encoding and the binary encoding. By combining an efficient fingerprinting method and a conventional multiple string matching algorithm, we can efficiently solve multiple pattern Cartesian tree matching. We propose three practical algorithms for multiple pattern Cartesian tree matching based on the Wu-Manber algorithm, the Rabin-Karp algorithm, and the Alpha Skip Search algorithm, respectively. In the experiments we compare our solutions against the previous algorithm [18]. Our solutions run faster than the previous algorithm as the pattern lengths increase. Especially, our algorithm based on Wu-Manber runs up to 33 times faster.
A full version of this paper is available at https://arxiv.org/abs/1911.01644. Gu, Song, and Park were supported by Collaborative Genome Program for Fostering New Post-Genome industry through the National Research Foundation of Korea (NRF) funded by the Ministry of Science ICT and Future Planning (No. NRF-2014M3C9A3063541).
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
References
Aho, A.V., Corasick, M.J.: Efficient string matching: an aid to bibliographic search. Commun. ACM 18(6), 333–340 (1975)
Berkman, O., Schieber, B., Vishkin, U.: Optimal doubly logarithmic parallel algorithms based on finding all nearest smaller values. J. Algorithms 14(3), 344–370 (1993)
Boyer, R.S., Moore, J.S.: A fast string searching algorithm. Commun. ACM 20(10), 762–772 (1977)
Charras, C., Lecroq, T., Pehoushek, J.D.: A very fast string matching algorithm for small alphabets and long patterns. In: Farach-Colton, M. (ed.) CPM 1998. LNCS, vol. 1448, pp. 55–64. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0030780
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). https://doi.org/10.1007/978-3-319-07959-2_26
Commentz-Walter, B.: A string matching algorithm fast on the average. In: Maurer, H.A. (ed.) ICALP 1979. LNCS, vol. 71, pp. 118–132. Springer, Heidelberg (1979). https://doi.org/10.1007/3-540-09510-1_10
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to algorithms second edition. The Knuth-Morris-Pratt Algorithm (2001)
Crochemore, M., Czumaj, A., Gasieniec, L., Lecroq, T., Plandowski, W., Rytter, W.: Fast practical multi-pattern matching. Inf. Process. Lett. 71(3–4), 107–113 (1999)
Ganguly, A., Hon, W.K., Sadakane, K., Shah, R., Thankachan, S.V., Yang, Y.: Space-efficient dictionaries for parameterized and order-preserving pattern matching. In: 27th Annual Symposium on Combinatorial Pattern Matching (CPM), pp. 2:1–2:12. LIPIcs (2016)
Han, M., Kang, M., Cho, S., Gu, G., Sim, J.S., Park, K.: Fast multiple order-preserving matching algorithms. In: Lipták, Z., Smyth, W.F. (eds.) IWOCA 2015. LNCS, vol. 9538, pp. 248–259. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29516-9_21
Hua, N., Song, H., Lakshman, T.: Variable-stride multi-pattern matching for scalable deep packet inspection. In: IEEE INFOCOM 2009, pp. 415–423. IEEE (2009)
Karp, R.M., Rabin, M.O.: Efficient randomized pattern-matching algorithms. IBM J. Res. Dev. 31(2), 249–260 (1987)
Kim, J., et al.: Order-preserving matching. Theor. Comput. Sci. 525, 68–79 (2014)
Knuth, D.E.: The Art of Computer Programming, volume 2: Seminumerical algorithms. Addison-Wesley Professional, Boston (2014)
Kubica, M., Kulczyński, T., Radoszewski, J., Rytter, W., Waleń, T.: A linear time algorithm for consecutive permutation pattern matching. Inf. Process. Let. 113(12), 430–433 (2013)
Liao, H.J., Lin, C.H.R., Lin, Y.C., Tung, K.Y.: Intrusion detection system: a comprehensive review. J. Netw. Comput. Appl. 36(1), 16–24 (2013)
Liu, J.N., Kwong, R.W.: Automatic extraction and identification of chart patterns towards financial forecast. Appl. Soft Comput. 7(4), 1197–1208 (2007)
Park, S., Amir, A., Landau, G.M., Park, K.: Cartesian tree matching and indexing. In: 30th Annual Symposium on Combinatorial Pattern Matching (CPM), pp. 16:1–16:14. LIPIcs (2019)
Song, S., Ryu, C., Faro, S., Lecroq, T., Park, K.: Fast cartesian tree matching. In: Brisaboa, N.R., Puglisi, S.J. (eds.) SPIRE 2019. LNCS, vol. 11811, pp. 124–137. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32686-9_9
Song, T., Zhang, W., Wang, D., Xue, Y.: A memory efficient multiple pattern matching architecture for network security. In: IEEE INFOCOM 2008-The 27th Conference on Computer Communications, pp. 166–170. IEEE (2008)
Vuillemin, J.: A unifying look at data structures. Commun. ACM 23(4), 229–239 (1980)
Wu, S., Manber, U.: A fast algorithm for multi-pattern searching. Technical report. TR-94-17, Department of Computer Science, University of Arizona (1994)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Gu, G., Song, S., Faro, S., Lecroq, T., Park, K. (2020). Fast Multiple Pattern Cartesian Tree Matching. In: Rahman, M., Sadakane, K., Sung, WK. (eds) WALCOM: Algorithms and Computation. WALCOM 2020. Lecture Notes in Computer Science(), vol 12049. Springer, Cham. https://doi.org/10.1007/978-3-030-39881-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-39881-1_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-39880-4
Online ISBN: 978-3-030-39881-1
eBook Packages: Computer ScienceComputer Science (R0)