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Dualities in Tree Representations

Authors Rayan Chikhi, Alexander Schönhuth

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Author Details

Rayan Chikhi
  • CNRS, Université de Lille, CRIStAL, Lille, France
Alexander Schönhuth
  • Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

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Rayan Chikhi and Alexander Schönhuth. Dualities in Tree Representations. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 18:1-18:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.CPM.2018.18

Abstract

A characterization of the tree T^* such that BP(T^*)=ova{DFUDS(T)}, the reversal of DFUDS(T) is given. An immediate consequence is a rigorous characterization of the tree T^ such that BP(T^)=DFUDS(T). In summary, BP and DFUDS are unified within an encompassing framework, which might have the potential to imply future simplifications with regard to queries in BP and/or DFUDS. Immediate benefits displayed here are to identify so far unnoted commonalities in most recent work on the Range Minimum Query problem, and to provide improvements for the Minimum Length Interval Query problem.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Trees
Keywords
  • Data Structures
  • Succinct Tree Representation
  • Balanced Parenthesis Representation
  • Isomorphisms

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References

  1. M. Bender and G. Farach-Colton. The LCA problem revisited. Proc. 4th LATIN, LNCS 1776:88-94, 2000. Google Scholar
  2. D. Benoit, E.D. Demaine, J.I. Munro, R. Raman, V. Raman, and S.S. Rao. Representing trees of higher degree. Algorithmica, 43(4):275-292, 2005. Google Scholar
  3. O. Berkman and U. Vishkin. Recursive star-tree parallel data structure. SIAM Journal of Computing, 22(2):221-242, 1993. Google Scholar
  4. R. Chikhi and A. Schönhuth. Dualities in Tree Representations. ArXiv e-prints, 2018. URL: http://arxiv.org/abs/1804.04263.
  5. Pooya Davoodi, Rajeev Raman, and Srinivasa Rao Satti. On succinct representations of binary trees. Mathematics in Computer Science, 11(2):177-189, 2017. URL: http://dx.doi.org/10.1007/s11786-017-0294-4.
  6. O. Delpratt, N. Rahman, and R. Raman. Engineering the LOUDS succinct tree representation. In Proc. of the WEA, LNCS 4007, pages 134-145, 2006. Google Scholar
  7. Arash Farzan, Rajeev Raman, and S. Srinivasa Rao. Universal succinct representations of trees? In Susanne Albers, Alberto Marchetti-Spaccamela, Yossi Matias, Sotiris E. Nikoletseas, and Wolfgang Thomas, editors, Automata, Languages and Programming, 36th International Colloquium, ICALP 2009, Rhodes, Greece, July 5-12, 2009, Proceedings, Part I, volume 5555 of Lecture Notes in Computer Science, pages 451-462. Springer, 2009. URL: http://dx.doi.org/10.1007/978-3-642-02927-1_38.
  8. H. Ferrada and G. Navarro. Improved range minimum queries. Journal of Discrete Algorithms, 43:72-80, 2017. Google Scholar
  9. J. Fischer and V. Heun. Space-efficient preprocessing schemes for range minimum queries on static arrays. SIAM Journal on Computing, 40(2):465-492, 2011. Google Scholar
  10. H.N. Gabow, J.L. Bentley, and R.E. Tarjan. Scaling and related techniques for geometry problems. In Proc. 16th STOC, pages 135-143, 1984. Google Scholar
  11. R. Grossi and G. Ottaviano. Design of practical succinct data structures for large data collections. In Proceedings of the 12th SEA, volume LNCS 7933, pages 5-17, 2013. Google Scholar
  12. X. Hu, J. Pei, and Y. Tao. Shortest unique queries on strings. In Proceedings of the International Symposium on String Processing and Information Retrieval (SPIRE), pages 161-172, 2014. Google Scholar
  13. G. Jacobson. Space-efficient static trees and graphs. In Proc. of the FOCS, pages 549-554, 1989. Google Scholar
  14. J. Jansson, K. Sadakane, and W.-K. Sung. Ultra-succinct representation of ordered trees. In Proc. of the SODA, pages 575-584, 2007. Google Scholar
  15. J.I. Munro and V. Raman. Succinct representation of balanced parentheses and static trees. SIAM Journal of Computing, 31(3):762-776, 2001. Google Scholar
  16. G. Navarro, Y. Nekrich, and L.M.S. Russo. Space-efficient data analysis queries on grids. Theoretical Computer Science, 482:60-72, 2013. Google Scholar
  17. G. Navarro and K. Sadakane. Fully-functional static and dynamic succinct trees. ACM Transactions on Algorithms, 10(3), 2014. Article 16. Google Scholar
  18. R. Raman, V. Raman, and S.R. Sattie. Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets. ACM Transactions on Algorithms, 3(4), 2007. Google Scholar
  19. Kunihiko Sadakane. Compressed suffix trees with full functionality. Theory of Computing Systems, 41(4):589-607, 2007. Google Scholar
  20. D. Tsur. Succinct representation of labeled trees. Technical Report 1312.6039, ArXiV, 2015. Google Scholar
  21. J. Vuillemin. A unifying look at data structures. Communications of the ACM, 4:229-239, 1980. Google Scholar
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