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Practical Parallel Block Tree Construction

Authors Robert Clausecker, Florian Kurpicz , Etienne Palanga

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ACM Subject Classification
  • Theory of computation → Shared memory algorithms
  • Theory of computation → Data compression
  • Computer systems organization → Single instruction, multiple data
Keywords
  • block tree
  • shared memory
  • compression
  • SIMD
  • Karp-Rabin fingerprints

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Abstract

The block tree [Belazzougui et al., J. Comput. Syst. Sci. '21] is a compressed representation of a length-n text that supports access, rank, and select queries while requiring only O(z log n/z) words of space, where z is the number of Lempel-Ziv factors of the text. In other words, its space requirements are asymptotically comparable to those of the compressed text itself. In practice, block trees offer query performance comparable to that of state-of-the-art compressed rank and select indices. However, their construction is significantly slower, and the fastest known construction algorithms additionally require a significant amount of working memory. To address these limitations, we propose fast and lightweight parallel algorithms for the efficient construction of block trees.
Our algorithm achieves similar construction speed than the currently fastest block tree construction algorithm on a single core and is up to eight times faster using 64 cores, while requiring an order of magnitude less memory. Overall, we achieve a speedup of up to 15.5 on 64 cores, which is in line with the parallel construction of the Lempel-Ziv compression.

Cite As Get BibTex

Robert Clausecker, Florian Kurpicz, and Etienne Palanga. Practical Parallel Block Tree Construction. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SEA.2026.13

Author Details

Robert Clausecker
  • Zuse Institute Berlin, Germany
Florian Kurpicz
  • University of Münster, Germany
Etienne Palanga
  • TU Dortmund University, Germany

Supplementary Materials

References

  1. Andreas Abel and Jan Reineke. uops.info: Characterizing latency, throughput, and port usage of instructions on intel microarchitectures. In ASPLOS, ASPLOS '19, pages 673-686, New York, NY, USA, 2019. ACM. URL: https://doi.org/10.1145/3297858.3304062.
  2. Dolev Adas and Roy Friedman. Brief announcement: Jiffy: A fast, memory efficient, wait-free multi-producers single-consumer queue. In DISC, volume 179 of LIPIcs, pages 50:1-50:3. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.DISC.2020.50.
  3. Mark Adler. pigz - parallel implementation of gzip. https://github.com/madler/pigz, 2024. Accessed: 2025-04-22.
  4. Jarno N. Alanko, Elena Biagi, Simon J. Puglisi, and Jaakko Vuohtoniemi. Subset wavelet trees. In SEA, volume 265 of LIPIcs, pages 4:1-4:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPIcs.SEA.2023.4.
  5. Maxim A. Babenko, Pawel Gawrychowski, Tomasz Kociumaka, and Tatiana Starikovskaya. Wavelet trees meet suffix trees. In SODA, pages 572-591. SIAM, 2015. URL: https://doi.org/10.1137/1.9781611973730.39.
  6. Djamal Belazzougui, Manuel Cáceres, Travis Gagie, Pawel Gawrychowski, Juha Kärkkäinen, Gonzalo Navarro, Alberto Ordóñez Pereira, Simon J. Puglisi, and Yasuo Tabei. Block trees. J. Comput. Syst. Sci., 117:1-22, 2021. URL: https://doi.org/10.1016/j.jcss.2020.11.002.
  7. Djamal Belazzougui, Patrick Hagge Cording, Simon J. Puglisi, and Yasuo Tabei. Access, rank, and select in grammar-compressed strings. In ESA, volume 9294 of Lecture Notes in Computer Science, pages 142-154. Springer, 2015. URL: https://doi.org/10.1007/978-3-662-48350-3_13.
  8. Djamal Belazzougui and Gonzalo Navarro. Optimal lower and upper bounds for representing sequences. ACM Trans. Algorithms, 11(4):31:1-31:21, 2015. URL: https://doi.org/10.1145/2629339.
  9. Timo Bingmann, Patrick Dinklage, Johannes Fischer, Florian Kurpicz, Enno Ohlebusch, and Peter Sanders. Scalable text index construction. In Algorithms for Big Data, volume 13201 of Lecture Notes in Computer Science, pages 252-284. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-21534-6_14.
  10. Antonio Boffa, Paolo Ferragina, and Giorgio Vinciguerra. A "learned" approach to quicken and compress rank/select dictionaries. In ALENEX, pages 46-59. SIAM, 2021. URL: https://doi.org/10.1137/1.9781611976472.4.
  11. Matteo Ceregini, Florian Kurpicz, and Rossano Venturini. Faster wavelet tree queries. Softw. Pract. Exp., 55(1):1931-1946, 2025. URL: https://doi.org/10.1002/spe.70013.
  12. Yu-Feng Chien, Wing-Kai Hon, Rahul Shah, Sharma V. Thankachan, and Jeffrey Scott Vitter. Geometric BWT: compressed text indexing via sparse suffixes and range searching. Algorithmica, 71(2):258-278, 2015. URL: https://doi.org/10.1007/S00453-013-9792-1.
  13. David R. Clark and J. Ian Munro. Efficient suffix trees on secondary storage (extended abstract). In SODA, pages 383-391. ACM/SIAM, 1996. URL: http://dl.acm.org/citation.cfm?id=313852.314087.
  14. Francisco Claude, Antonio Fariña, Miguel A. Martínez-Prieto, and Gonzalo Navarro. Universal indexes for highly repetitive document collections. Inf. Syst., 61:1-23, 2016. URL: https://doi.org/10.1016/J.IS.2016.04.002.
  15. Francisco Claude and Gonzalo Navarro. Improved grammar-based compressed indexes. In SPIRE, volume 7608 of Lecture Notes in Computer Science, pages 180-192. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-34109-0_19.
  16. Francisco Claude, Gonzalo Navarro, and Alberto Ordóñez Pereira. The wavelet matrix: An efficient wavelet tree for large alphabets. Inf. Syst., 47:15-32, 2015. URL: https://doi.org/10.1016/j.is.2014.06.002.
  17. Richard Cole. Parallel merge sort. SIAM J. Comput., 17(4):770-785, 1988. URL: https://doi.org/10.1137/0217049.
  18. Richard Cole and Uzi Vishkin. Faster optimal parallel prefix sums and list ranking. Inf. Comput., 81(3):334-352, 1989. URL: https://doi.org/10.1016/0890-5401(89)90036-9.
  19. Patrick Dinklage, Jonas Ellert, Johannes Fischer, Florian Kurpicz, and Marvin Löbel. Practical wavelet tree construction. ACM J. Exp. Algorithmics, 26:1.8:1-1.8:67, 2021. URL: https://doi.org/10.1145/3457197.
  20. Patrick Dinklage, Johannes Fischer, and Florian Kurpicz. Constructing the wavelet tree and wavelet matrix in distributed memory. In ALENEX, pages 214-228. SIAM, 2020. URL: https://doi.org/10.1137/1.9781611976007.17.
  21. Patrick Dinklage, Johannes Fischer, Florian Kurpicz, and Jan-Philipp Tarnowski. Bit-parallel (compressed) wavelet tree construction. In DCC, pages 81-90. IEEE, 2023. URL: https://doi.org/10.1109/DCC55655.2023.00016.
  22. Jonas Ellert, Johannes Fischer, and Nodari Sitchinava. Lcp-aware parallel string sorting. In Euro-Par, volume 12247 of Lecture Notes in Computer Science, pages 329-342. Springer, 2020. URL: https://doi.org/10.1007/978-3-030-57675-2_21.
  23. Jonas Ellert and Florian Kurpicz. Parallel external memory wavelet tree and wavelet matrix construction. In SPIRE, volume 11811 of Lecture Notes in Computer Science, pages 392-406. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-32686-9_28.
  24. Paolo Ferragina, Raffaele Giancarlo, and Giovanni Manzini. The myriad virtues of wavelet trees. Inf. Comput., 207(8):849-866, 2009. URL: https://doi.org/10.1016/j.ic.2008.12.010.
  25. Paolo Ferragina, Giovanni Manzini, Veli Mäkinen, and Gonzalo Navarro. An alphabet-friendly fm-index. In SPIRE, volume 3246 of Lecture Notes in Computer Science, pages 150-160. Springer, 2004. URL: https://doi.org/10.1007/978-3-540-30213-1_23.
  26. Paolo Ferragina, Giovanni Manzini, Veli Mäkinen, and Gonzalo Navarro. Compressed representations of sequences and full-text indexes. ACM Trans. Algorithms, 3(2):20, 2007. URL: https://doi.org/10.1145/1240233.1240243.
  27. Johannes Fischer, Florian Kurpicz, and Marvin Löbel. Simple, fast and lightweight parallel wavelet tree construction. In ALENEX, pages 9-20. SIAM, 2018. URL: https://doi.org/10.1137/1.9781611975055.2.
  28. José Fuentes-Sepúlveda, Erick Elejalde, Leo Ferres, and Diego Seco. Parallel construction of wavelet trees on multicore architectures. Knowl. Inf. Syst., 51(3):1043-1066, 2017. URL: https://doi.org/10.1007/s10115-016-1000-6.
  29. Simon Gog and Matthias Petri. Optimized succinct data structures for massive data. Softw. Pract. Exp., 44(11):1287-1314, 2014. URL: https://doi.org/10.1002/SPE.2198.
  30. Tal Goldberg and Uri Zwick. Optimal deterministic approximate parallel prefix sums and their applications. In ISTCS, pages 220-228. IEEE Computer Society, 1995. URL: https://doi.org/10.1109/ISTCS.1995.377028.
  31. Rodrigo González, Szymon Grabowski, Veli Mäkinen, and Gonzalo Navarro. Practical implementation of rank and select queries. In WEA, pages 27-38, 2005. Google Scholar
  32. Roberto Grossi, Ankur Gupta, and Jeffrey Scott Vitter. High-order entropy-compressed text indexes. In SODA, pages 841-850. ACM/SIAM, 2003. URL: http://dl.acm.org/citation.cfm?id=644108.644250.
  33. Roberto Grossi, Jeffrey Scott Vitter, and Bojian Xu. Wavelet trees: From theory to practice. In CCP, pages 210-221. IEEE Computer Society, 2011. URL: https://doi.org/10.1109/CCP.2011.16.
  34. Aaron Hong, Christina Boucher, Travis Gagie, Yansong Li, and Norbert Zeh. Another virtue of wavelet forests. In SPIRE, volume 14899 of Lecture Notes in Computer Science, pages 184-191. Springer, 2024. URL: https://doi.org/10.1007/978-3-031-72200-4_14.
  35. Guy Jacobson. Space-efficient static trees and graphs. In FOCS, pages 549-554. IEEE Computer Society, 1989. URL: https://doi.org/10.1109/SFCS.1989.63533.
  36. Richard M. Karp and Michael O. Rabin. Efficient randomized pattern-matching algorithms. IBM J. Res. Dev., 31(2):249-260, 1987. URL: https://doi.org/10.1147/rd.312.0249.
  37. Dominik Kempa and Tomasz Kociumaka. Collapsing the hierarchy of compressed data structures: Suffix arrays in optimal compressed space. In FOCS, pages 1877-1886. IEEE, 2023. URL: https://doi.org/10.1109/FOCS57990.2023.00114.
  38. John C. Kieffer and En-Hui Yang. Grammar-based codes: A new class of universal lossless source codes. IEEE Trans. Inf. Theory, 46(3):737-754, 2000. URL: https://doi.org/10.1109/18.841160.
  39. Tomasz Kociumaka, Gonzalo Navarro, and Nicola Prezza. Towards a definitive measure of repetitiveness. In LATIN, volume 12118 of Lecture Notes in Computer Science, pages 207-219. Springer, 2020. URL: https://doi.org/10.1007/978-3-030-61792-9_17.
  40. Dominik Köppl, Florian Kurpicz, and Daniel Meyer. Faster block tree construction. In ESA, volume 274 of LIPIcs, pages 74:1-74:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPIcs.ESA.2023.74.
  41. Dominik Köppl, Gonzalo Navarro, and Nicola Prezza. HOLZ: high-order entropy encoding of lempel-ziv factor distances. In DCC, pages 83-92. IEEE, 2022. URL: https://doi.org/10.1109/DCC52660.2022.00016.
  42. S. Rao Kosaraju and Giovanni Manzini. Compression of low entropy strings with lempel-ziv algorithms. SIAM J. Comput., 29(3):893-911, 1999. URL: https://doi.org/10.1137/S0097539797331105.
  43. Florian Kurpicz. Engineering compact data structures for rank and select queries on bit vectors. In SPIRE, volume 13617 of Lecture Notes in Computer Science, pages 257-272. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-20643-6_19.
  44. Florian Kurpicz. pasta-toolbox/block_tree: v0.1.0, July 2023. URL: https://doi.org/10.5281/zenodo.8114255.
  45. Florian Kurpicz, Niccolò Rigi-Luperti, and Peter Sanders. Theory meets practice for bit vectors supporting rank and select. CoRR, abs/2509.17819, 2025. URL: https://doi.org/10.48550/arXiv.2509.17819.
  46. Julian Labeit, Julian Shun, and Guy E. Blelloch. Parallel lightweight wavelet tree, suffix array and fm-index construction. J. Discrete Algorithms, 43:2-17, 2017. URL: https://doi.org/10.1016/j.jda.2017.04.001.
  47. Christos Makris. Wavelet trees: A survey. Comput. Sci. Inf. Syst., 9(2):585-625, 2012. URL: https://doi.org/10.2298/CSIS110606004M.
  48. Stefano Marchini and Sebastiano Vigna. Compact fenwick trees for dynamic ranking and selection. Softw. Pract. Exp., 50(7):1184-1202, 2020. URL: https://doi.org/10.1002/spe.2791.
  49. Masaki Matsushita and Yasushi Inoguchi. Parallel processing of grammar compression. In DCC, page 358. IEEE, 2021. URL: https://doi.org/10.1109/DCC50243.2021.00068.
  50. Masaki Matsushita and Yasushi Inoguchi. Applying practical parallel grammar compression to large-scale data. In DCC, page 473. IEEE, 2022. URL: https://doi.org/10.1109/DCC52660.2022.00084.
  51. Frank McSherry, Michael Isard, and Derek Gordon Murray. Scalability! but at what cost? In HotOS. USENIX Association, 2015. URL: https://www.usenix.org/conference/hotos15/workshop-program/presentation/mcsherry.
  52. J. Ian Munro, Yakov Nekrich, and Jeffrey Scott Vitter. Fast construction of wavelet trees. Theor. Comput. Sci., 638:91-97, 2016. URL: https://doi.org/10.1016/j.tcs.2015.11.011.
  53. Gonzalo Navarro. Wavelet trees for all. J. Discrete Algorithms, 25:2-20, 2014. URL: https://doi.org/10.1016/j.jda.2013.07.004.
  54. Gonzalo Navarro. Indexing highly repetitive string collections, part I: repetitiveness measures. ACM Comput. Surv., 54(2):29:1-29:31, 2022. URL: https://doi.org/10.1145/3434399.
  55. Gonzalo Navarro and Veli Mäkinen. Compressed full-text indexes. ACM Comput. Surv., 39(1):2-es, 2007. URL: https://doi.org/10.1145/1216370.1216372.
  56. Gonzalo Navarro and Eliana Providel. Fast, small, simple rank/select on bitmaps. In SEA, volume 7276 of Lecture Notes in Computer Science, pages 295-306. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-30850-5_26.
  57. Daisuke Okanohara and Kunihiko Sadakane. Practical entropy-compressed rank/select dictionary. In ALENEX. SIAM, 2007. URL: https://doi.org/10.1137/1.9781611972870.6.
  58. Alberto Ordóñez Pereira, Gonzalo Navarro, and Nieves R. Brisaboa. Grammar compressed sequences with rank/select support. J. Discrete Algorithms, 43:54-71, 2017. URL: https://doi.org/10.1016/J.JDA.2016.10.001.
  59. Giulio Ermanno Pibiri and Shunsuke Kanda. Rank/select queries over mutable bitmaps. Inf. Syst., 99:101756, 2021. URL: https://doi.org/10.1016/j.is.2021.101756.
  60. Mihai Pǎtraşku. Succincter. In FOCS, pages 305-313. IEEE Computer Society, 2008. URL: https://doi.org/10.1109/FOCS.2008.83.
  61. Rajeev Raman, Venkatesh Raman, and Srinivasa Rao Satti. Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets. ACM Trans. Algorithms, 3(4):43, 2007. URL: https://doi.org/10.1145/1290672.1290680.
  62. Jindřich Nový. pxz - Parallel XZ compressor, 2024. Accessed: 2025-04-22. URL: https://github.com/jnovy/pxz.
  63. Wojciech Rytter. Application of Lempel-Ziv factorization to the approximation of grammar-based compression. Theor. Comput. Sci., 302(1-3):211-222, 2003. URL: https://doi.org/10.1016/S0304-3975(02)00777-6.
  64. Julian Shun and Fuyao Zhao. Practical parallel lempel-ziv factorization. In DCC, pages 123-132. IEEE, 2013. URL: https://doi.org/10.1109/DCC.2013.20.
  65. Sebastiano Vigna. Broadword implementation of rank/select queries. In WEA, volume 5038 of Lecture Notes in Computer Science, pages 154-168. Springer, 2008. URL: https://doi.org/10.1007/978-3-540-68552-4_12.
  66. Kaneta Y. Fast wavelet tree construction in practice. In SPIRE, volume 11147 of Lecture Notes in Computer Science, pages 218-232. Springer, 2018. URL: https://doi.org/10.1007/978-3-030-00479-8_18.
  67. Dong Zhou, David G. Andersen, and Michael Kaminsky. Space-efficient, high-performance rank and select structures on uncompressed bit sequences. In SEA, volume 7933 of Lecture Notes in Computer Science, pages 151-163. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-38527-8_15.
  68. Jacob Ziv and Abraham Lempel. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory, 23(3):337-343, 1977. URL: https://doi.org/10.1109/TIT.1977.1055714.
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