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Alphabet-Dependent String Searching with Wexponential Search Trees

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Combinatorial Pattern Matching (CPM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9133))

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Abstract

We consider finding a pattern of length \(m\) in a compacted (linear-size) trie storing strings over an alphabet of size \(\sigma \). In static tries, we achieve \(O(m+\lg \lg \sigma )\) deterministic time, whereas in dynamic tries we achieve \(O(m+\frac{\lg ^{2}\lg \sigma }{\lg \lg \lg \sigma })\) deterministic time per query or update. One particular application of the above bounds (static and dynamic) are suffix trees, where we also show how to pre- or append letters in \(O(\lg \lg n + \frac{\lg ^{2}\lg \sigma }{\lg \lg \lg \sigma })\) time. Our main technical contribution is a weighted variant of exponential search trees, which might be of independent interest.

P. Gawrychowski—Currently holding a post-doc position at Warsaw Center of Mathematics and Computer Science.

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References

  1. Amir, A., Franceschini, G., Grossi, R., Kopelowitz, T., Lewenstein, M., Lewenstein, N.: Managing unbounded-length keys in comparison-driven data structures with applications to online indexing. SIAM J. Comput. 43(4), 1396–1416 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  2. Andersson, A., Thorup, M.: Dynamic ordered sets with exponential search trees. J. ACM 53(3) (2007). Article No. 13

    Google Scholar 

  3. Beame, P., Fich, F.E.: Optimal bounds for the predecessor problem and related problems. J. Comput. Syst. Sci. 65(1), 38–72 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bender, M.A., Cole, R., Raman, R.: Exponential structures for efficient cache-oblivious algorithms. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 195–207. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  5. Breslauer, D., Italiano, G.F.: Near real-time suffix tree construction via the fringe marked ancestor problem. J. Discrete Algorithms 18, 32–48 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cole, R., Kopelowitz, T., Lewenstein, M.: Suffix trays and suffix trists: structures for faster text indexing. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 358–369. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Fischer, J., Gawrychowski, P.: Alphabet-dependent string searching with wexponential search trees. CoRR abs/1302.3347 (2013). http://arxiv.org/abs/1302.3347

  8. Fredman, M.L., Komlós, J., Szemerédi, E.: Storing a sparse table with \({O}(1)\) worst case access time. J. ACM 31(3), 538–544 (1984)

    Article  MATH  Google Scholar 

  9. Kopelowitz, T.: On-line indexing for general alphabets via predecessor queries on subsets of an ordered list. In: Proceedings of the FOCS, pp. 283–292. IEEE Computer Society (2012)

    Google Scholar 

  10. Kucherov, G., Nekrich, Y.: Full-fledged real-time indexing for constant size alphabets. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part I. LNCS, vol. 7965, pp. 650–660. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  11. Manber, U., Myers, E.W.: Suffix arrays: a new method for on-line string searches. SIAM J. Comput. 22(5), 935–948 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  12. McCreight, E.M.: A space-economical suffix tree construction algorithm. J. ACM 23(2), 262–272 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  13. Mehlhorn, K.: Dynamic binary search. SIAM J. Comput. 8(2), 175–198 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  14. Ružić, M.: Constructing efficient dictionaries in close to sorting time. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 84–95. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  15. Weiner, P.: Linear pattern matching algorithms. In: Proceedings of the Annual Symposium on Switching and Automata Theory, pp. 1–11. IEEE Computer Society (1973)

    Google Scholar 

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Author information

Authors and Affiliations

  1. TU Dortmund, Dortmund, Germany

    Johannes Fischer

  2. University of Warsaw, Warsaw, Poland

    Paweł Gawrychowski

Authors
  1. Johannes Fischer
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  2. Paweł Gawrychowski
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Corresponding author

Correspondence to Johannes Fischer .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Ferdinando Cicalese

  2. Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

    Ely Porat

  3. Department of Computer Science, University of Salerno, Fisciano, Italy

    Ugo Vaccaro

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Fischer, J., Gawrychowski, P. (2015). Alphabet-Dependent String Searching with Wexponential Search Trees. In: Cicalese, F., Porat, E., Vaccaro, U. (eds) Combinatorial Pattern Matching. CPM 2015. Lecture Notes in Computer Science(), vol 9133. Springer, Cham. https://doi.org/10.1007/978-3-319-19929-0_14

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  • DOI: https://doi.org/10.1007/978-3-319-19929-0_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19928-3

  • Online ISBN: 978-3-319-19929-0

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