Abstract
Cartesian tree is a fundamental data structure with many applications in the areas of data structures and string processing. In this paper, we study the construction of a Cartesian tree on a parallel computation model. We present a CREW PRAM algorithm that runs in O(logn) parallel time and has linear work and space. This improves upon the best previous result of Blelloch and Shun which takes O(log2 n) time and linear work/space.
This work is supported by the Research Grants Council of Hong Kong under grant 9041688 (CityU 124411).
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References
Berkman, O., Schieber, B., Vishkin, U.: Optimal doubly logarithmic parallel algorithms based on finding all nearest smaller values. Journal of Algorithms 14, 371–380 (1993)
Blelloch, G.E., Shun, J.: A simple parallel cartesian tree algorithm and its application to suffix tree construction. In: ALENEX 2011, pp. 48–58 (2011)
Demaine, E.D., Landau, G.M., Weimann, O.: On Cartesian trees and range minimum queries. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part I. LNCS, vol. 5555, pp. 341–353. Springer, Heidelberg (2009)
Gabow, H., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for goemetry problems. In: Proceedings of the Sixteenth Annual ACM Symposium on Theory of Computing, pp. 135–143. ACM (1984)
Gusfield, D.: Algorithms on strings, trees and sequences. Cambridge University Press (1997)
Iliopoulos, C., Rytter, W.: On parallel transformations of suffix arrays into suffix trees. In: 15th Australasian Workshop on Combinatorial Algorithms (2004)
Jaja, J.: An introduction to parallel algorithms. Addison-Wesley Professional (1992)
Shiloach, Y., Vishkin, U.: Finding the maximum, merging and sorting in a parallel computation model. Journal of Algorithms 2(1), 88–102 (1981)
Vuillemin, J.: A unifying look at data structures. Communications of the ACM 23(4), 229–239 (1980)
Yuan, H., Atallah, M.J.: Data structures for range minimum queries in multidimensional arrays. In: Proceedings of the Twenty-first Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 150–160 (2010)
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Poon, C.K., Yuan, H. (2013). A Faster CREW PRAM Algorithm for Computing Cartesian Trees. In: Spirakis, P.G., Serna, M. (eds) Algorithms and Complexity. CIAC 2013. Lecture Notes in Computer Science, vol 7878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38233-8_28
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DOI: https://doi.org/10.1007/978-3-642-38233-8_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38232-1
Online ISBN: 978-3-642-38233-8
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