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Graph Indexing Beyond Wheeler Graphs

Authors Jarno N. Alanko , Elena Biagi , Massimo Equi , Veli Mäkinen , Simon J. Puglisi , Nicola Rizzo , Kunihiko Sadakane , Jouni Sirén

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Subject Classification

ACM Subject Classification
  • Theory of computation → Sorting and searching
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Pattern matching
  • Theory of computation → Formal languages and automata theory
Keywords
  • indexing
  • compression
  • compressed data structures
  • string algorithms
  • pattern matching

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Abstract

After the discovery of the FM index, which linked the Burrows-Wheeler transform (BWT) to pattern matching on strings, several contemporaneous strands of research began on indexing more complex structures with the BWT, such as tries, finite languages, de Bruijn graphs, and aligned sequences. These directions can now be viewed as culminating in the theory of Wheeler Graphs, but sometimes they go beyond. This chapter reviews the significant body of "proto Wheeler Graph" indexes, many of which exploit characteristics of their specific case to outperform Wheeler graphs, especially in practice.

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Jarno N. Alanko, Elena Biagi, Massimo Equi, Veli Mäkinen, Simon J. Puglisi, Nicola Rizzo, Kunihiko Sadakane, and Jouni Sirén. Graph Indexing Beyond Wheeler Graphs. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 13:1-13:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.Manzini.13

Author Details

Jarno N. Alanko
  • Department of Computer Science, University of Helsinki, Finland
Elena Biagi
  • Department of Computer Science, University of Helsinki, Finland
Massimo Equi
  • Department of Computer Science, Aalto University, Finland
Veli Mäkinen
  • Department of Computer Science, University of Helsinki, Finland
Simon J. Puglisi
  • Department of Computer Science, University of Helsinki, Finland
Nicola Rizzo
  • Department of Computer Science, University of Helsinki, Finland
Kunihiko Sadakane
  • Department of Mathematical Informatics, University of Tokyo, Japan
Jouni Sirén
  • Genomics Institute, University of California, Santa Cruz, CA, USA

Funding

  • Alanko, Jarno N.: Funded by the Helsinki Institute for Information Technology (HIIT).
  • Biagi, Elena: Funded by the Academy of Finland via grant 339070.
  • Equi, Massimo: Partially funded by the Research Council of Finland, Grant 359104.
  • Mäkinen, Veli: Partially funded by the European Union’s Horizon Europe research and innovation programme under grant agreement No 101060011 (TeamPerMed).
  • Puglisi, Simon J.: Funded by the Academy of Finland via grant 339070.
  • Rizzo, Nicola: Funded by the European Union’s Horizon Europe research and innovation programme under grant agreement No 101060011 (TeamPerMed).
  • Sirén, Jouni: Funded by the National Human Genome Research Institute (NHGRI) under award numbers U01HG013748 and U41HG010972.

Acknowledgements

We wish to thank Hideo Bannai for spotting a mistake in the original version of Definition 22.

References

  1. Jarno Alanko, Giovanna D'Agostino, Alberto Policriti, and Nicola Prezza. Regular languages meet prefix sorting. In Proc. SODA 2020, pages 911-930. SIAM, 2020. URL: https://doi.org/10.1137/1.9781611975994.55.
  2. Jarno Alanko, Giovanna D'Agostino, Alberto Policriti, and Nicola Prezza. Wheeler languages. Information and Computation, 281:104820, 2021. URL: https://doi.org/10.1016/j.ic.2021.104820.
  3. Jarno N. Alanko, Elena Biagi, and Simon J. Puglisi. Longest common prefix arrays for succinct k-spectra. In Proc. SPIRE, LNCS 14240, pages 1-13. Springer, 2023. URL: https://doi.org/10.1007/978-3-031-43980-3_1.
  4. Jarno N. Alanko, Elena Biagi, Simon J. Puglisi, and Jaakko Vuohtoniemi. Subset wavelet trees. In Proc. of the 21st International Symposium on Experimental Algorithms (SEA), LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPICS.SEA.2023.4.
  5. Jarno N. Alanko, Simon J. Puglisi, and Jaakko Vuohtoniemi. Small searchable k-spectra via subset rank queries on the spectral Burrows-Wheeler transform. In Proc. ACDA, pages 225-236. SIAM, 2023. URL: https://doi.org/10.1137/1.9781611977714.20.
  6. Jarno N. Alanko, Jaakko Vuohtoniemi, Tommi Mäklin, and Simon J. Puglisi. Themisto: a scalable colored k-mer index for sensitive pseudoalignment against hundreds of thousands of bacterial genomes. Bioinform., 39(Supplement-1):260-269, 2023. URL: https://doi.org/10.1093/BIOINFORMATICS/BTAD233.
  7. Uwe Baier. On undetected redundancy in the Burrows-Wheeler transform. In Proc. CPM 2018, volume 105 of LIPIcs, pages 3:1-3:15, 2018. URL: https://doi.org/10.4230/LIPIcs.CPM.2018.3.
  8. Andrej Baláž, Travis Gagie, Adrián Goga, Simon Heumos, Gonzalo Navarro, Alessia Petescia, and Jouni Sirén. Wheeler maps. In Proc. LATIN 2024, volume 14578 of LNCS, pages 178-192. Springer, 2024. URL: https://doi.org/10.1007/978-3-031-55598-5_12.
  9. Christina Boucher, Alex Bowe, Travis Gagie, Simon J. Puglisi, and Kunihiko Sadakane. Variable-order de Bruijn graphs. In Proc. DCC 2015, pages 383-392. IEEE, 2015. URL: https://doi.org/10.1109/DCC.2015.70.
  10. Alexander Bowe, Taku Onodera, Kunihiko Sadakane, and Tetsuo Shibuya. Succinct de Bruijn graphs. In International workshop on algorithms in bioinformatics, pages 225-235. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-33122-0_18.
  11. Michael Burrows and David J. Wheeler. A block sorting lossless data compression algorithm. Technical Report 124, Digital Equipment Corporation, 1994. URL: http://www.hpl.hp.com/techreports/Compaq-DEC/SRC-RR-124.html.
  12. Bastien Cazaux and Eric Rivals. Linking BWT and XBW via Aho-Corasick automaton: Applications to run-length encoding. In Proc. CPM 2019, volume 128 of LIPIcs, pages 24:1-24:20, 2019. URL: https://doi.org/10.4230/LIPIcs.CPM.2019.24.
  13. Rayan Chikhi, Antoine Limasset, and Paul Medvedev. Compacting de bruijn graphs from sequencing data quickly and in low memory. Bioinform., 32(12):201-208, 2016. URL: https://doi.org/10.1093/BIOINFORMATICS/BTW279.
  14. David R. Clark and J. Ian Munro. Efficient suffix trees on secondary storage (extended abstract). In Proc. SODA 1996, pages 383-391. SIAM, 1996. URL: https://doi.org/10.1145/313852.314087.
  15. Alessio Conte, Nicola Cotumaccio, Travis Gagie, Giovanni Manzini, Nicola Prezza, and Marinella Sciortino. Computing matching statistics on Wheeler DFAs. In Proc. DCC 2023, pages 150-159. IEEE, 2023. URL: https://doi.org/10.1109/DCC55655.2023.00023.
  16. Nicola Cotumaccio, Giovanna D'Agostino, Alberto Policriti, and Nicola Prezza. Co-lexicographically ordering automata and regular languages - part I. Journal of the ACM, 70(4):1-73, 2023. URL: https://doi.org/10.1145/3607471.
  17. Massimo Equi, Roberto Grossi, Veli Mäkinen, and Alexandru I. Tomescu. On the complexity of string matching for graphs. In 46th International Colloquium on Automata, Languages, and Programming (ICALP), volume 132 of LIPIcs, pages 55:1-55:15, 2019. URL: https://doi.org/10.4230/LIPICS.ICALP.2019.55.
  18. Massimo Equi, Veli Mäkinen, and Alexandru I. Tomescu. Graphs cannot be indexed in polynomial time for sub-quadratic time string matching, unless SETH fails. Theor. Comput. Sci., 975:114128, 2023. URL: https://doi.org/10.1016/J.TCS.2023.114128.
  19. Massimo Equi, Veli Mäkinen, Alexandru I. Tomescu, and Roberto Grossi. On the complexity of string matching for graphs. ACM Trans. Algorithms, 19(3):21:1-21:25, 2023. URL: https://doi.org/10.1145/3588334.
  20. Massimo Equi, Tuukka Norri, Jarno Alanko, Bastien Cazaux, Alexandru I. Tomescu, and Veli Mäkinen. Algorithms and complexity on indexing founder graphs. Algorithmica, 85(6):1586-1623, 2023. URL: https://doi.org/10.1007/S00453-022-01007-W.
  21. Paolo Ferragina, Fabrizio Luccio, Giovanni Manzini, and S. Muthukrishnan. Compressing and indexing labeled trees, with applications. Journal of the ACM, 57(1):4, 2009. URL: https://doi.org/10.1145/1613676.1613680.
  22. Paolo Ferragina and Giovanni Manzini. Indexing compressed text. Journal of the ACM, 52(4):552-581, 2005. URL: https://doi.org/10.1145/1082036.1082039.
  23. Johannes Fischer, Veli Mäkinen, and Gonzalo Navarro. Faster entropy-bounded compressed suffix trees. Theoretical Computer Science, 410(51):5354-5364, 2009. URL: https://doi.org/10.1016/j.tcs.2009.09.012.
  24. Travis Gagie, Aleksi Hartikainen, Kalle Karhu, Juha Kärkkäinen, Gonzalo Navarro, Simon J. Puglisi, and Jouni Sirén. Document retrieval on repetitive string collections. Information Retrieval Journal, 20(3):253-291, 2017. URL: https://doi.org/10.1007/s10791-017-9297-7.
  25. Travis Gagie, Giovanni Manzini, and Jouni Sirén. Wheeler graphs: A framework for BWT-based data structures. Theoretical Computer Science, 698:67-78, 2017. URL: https://doi.org/10.1016/J.TCS.2017.06.016.
  26. Erik Garrison, Jouni Sirén, Adam M. Novak, Glenn Hickey, Jordan M. Eizenga, Eric T. Dawson, William Jones, Shilpa Garg, Charles Markello, Michael F. Lin, Benedict Paten, and Richard Durbin. Variation graph toolkit improves read mapping by representing genetic variation in the reference. Nature Biotechnology, 36(9):875-879, 2018. URL: https://doi.org/10.1038/nbt.4227.
  27. Daniel Gibney and Sharma V. Thankachan. On the complexity of recognizing wheeler graphs. Algorithmica, 84(3):784-814, 2022. URL: https://doi.org/10.1007/S00453-021-00917-5.
  28. 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.
  29. Roberto Grossi, Ankur Gupta, and Jeffrey Scott Vitter. High-order entropy-compressed text indexes. In Proc. SODA 2003, pages 841-850. SIAM, 2003. URL: http://dl.acm.org/citation.cfm?id=644108.644250.
  30. Roberto Grossi, Costas S. Iliopoulos, Chang Liu, Nadia Pisanti, Solon P. Pissis, Ahmad Retha, Giovanna Rosone, Fatima Vayani, and Luca Versari. On-line pattern matching on similar texts. In Proc. CPM 2017, volume 78 of LIPIcs, pages 9:1-9:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPICS.CPM.2017.9.
  31. Roberto Grossi and Jeffrey Scott Vitter. Compressed suffix arrays and suffix trees with applications to text indexing and string matching. SIAM Journal on Computing, 35(2):378-407, 2005. URL: https://doi.org/10.1137/S0097539702402354.
  32. Lin Huang, Victoria Popic, and Serafim Batzoglou. Short read alignment with populations of genomes. Bioinformatics, 29(13):i361-i370, 2013. URL: https://doi.org/10.1093/bioinformatics/btt215.
  33. Songbo Huang, T.W. Lam, W.K. Sung, S.L. Tam, and S.M. Yiu. Indexing similar DNA sequences. In Proc. AAIM 2010, volume 6124 of LNCS, pages 180-190. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-14355-7_19.
  34. Sorina Maciuca, Carlos del Ojo Elias, Gil McVean, and Zamin Iqbal. A natural encoding of genetic variation in a Burrows-Wheeler transform to enable mapping and genome inference. In Proc. WABI 2016, volume 9838 of LNCS, pages 222-233. Springer, 2016. URL: https://doi.org/10.1007/978-3-319-43681-4_18.
  35. Giovanni Manzini. XBWT tricks. In Proc. SPIRE 2016, volume 9954 of LNCS, pages 80-92. Springer, 2016. URL: https://doi.org/10.1007/978-3-319-46049-9_8.
  36. Miguel A. Martínez-Prieto, Nieves Brisaboa, Rodrigo Cánovas, Francisco Claude, and Gonzalo Navarro. Practical compressed string dictionaries. Information Systems, 56:73-108, 2016. URL: https://doi.org/10.1016/j.is.2015.08.008.
  37. J. Ian Munro. Tables. In Proc. FSTTCS 1996, volume 1180 of LNCS. Springer, 1996. URL: https://doi.org/10.1007/3-540-62034-6_35.
  38. Veli Mäkinen, Gonzalo Navarro, Jouni Sirén, and Niko Välimäki. Storage and retrieval of highly repetitive sequence collections. Journal of Computational Biology, 17(3):281-308, 2010. URL: https://doi.org/10.1089/cmb.2009.0169.
  39. Joong Chae Na, Hyunjoon Kim, Seunghwan Min, Heejin Park, Thierry Lecroq, Martine Léonard, Laurent Mouchard, and Kunsoo Park. FM-index of alignment with gaps. Theoretical Computer Science, 710:148-157, 2018. URL: https://doi.org/10.1016/j.tcs.2017.02.020.
  40. Joong Chae Na, Hyunjoon Kim, Heejin Park, Thierry Lecroq, Martine Léonard, Laurent Mouchard, and Kunsoo Park. FM-index of alignment: A compressed index for similar strings. Theoretical Computer Science, 638:159-170, 2016. URL: https://doi.org/10.1016/j.tcs.2015.08.008.
  41. Enno Ohlebusch, Simon Gog, and Adrian Kügel. Computing matching statistics and maximal exact matches on compressed full-text indexes. In Proc. SPIRE 2010, volume 6393 of LNCS, pages 347-358. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-16321-0_36.
  42. Daisuke Okanohara and Kunihiko Sadakane. Practical entropy-compressed rank/select dictionary. In Proc. ALENEX 2007, pages 60-70. SIAM, 2007. URL: https://doi.org/10.1137/1.9781611972870.6.
  43. Nicola Rizzo, Massimo Equi, Tuukka Norri, and Veli Mäkinen. Elastic founder graphs improved and enhanced. Theor. Comput. Sci., 982:114269, 2024. URL: https://doi.org/10.1016/J.TCS.2023.114269.
  44. Kunihiko Sadakane. Succinct data structures for flexible text retrieval systems. Journal of Discrete Algorithms, 5(1):12-22, 2007. URL: https://doi.org/10.1016/j.jda.2006.03.011.
  45. Jouni Sirén. Sampled longest common prefix array. In Proc. CPM 2010, volume 6129 of LNCS, pages 227-237. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-13509-5_21.
  46. Jouni Sirén. Indexing variation graphs. In Proc. ALENEX 2017, pages 13-27. SIAM, 2017. URL: https://doi.org/10.1137/1.9781611974768.2.
  47. Jouni Sirén, Erik Garrison, Adam M. Novak, Benedict Paten, and Richard Durbin. Haplotype-aware graph indexes. Bioinformatics, 36(2):400-407, 2020. URL: https://doi.org/10.1093/bioinformatics/btz575.
  48. Jouni Sirén, Niko Välimäki, and Veli Mäkinen. Indexing finite language representation of population genotypes. In Proc. WABI 2011, volume 6833 of LNCS, pages 270-281. Springer, 2011. URL: https://doi.org/10.1007/978-3-642-23038-7_23.
  49. Jouni Sirén, Niko Välimäki, and Veli Mäkinen. Indexing graphs for path queries with applications in genome research. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 11(2):375-388, 2014. URL: https://doi.org/10.1109/TCBB.2013.2297101.
  50. Esko Ukkonen. Finding founder sequences from a set of recombinants. In Roderic Guigó and Dan Gusfield, editors, Algorithms in Bioinformatics, Second International Workshop, WABI 2002, Rome, Italy, September 17-21, 2002, Proceedings, volume 2452 of Lecture Notes in Computer Science, pages 277-286. Springer, 2002. URL: https://doi.org/10.1007/3-540-45784-4_21.
  51. Ryan Williams. A new algorithm for optimal 2-constraint satisfaction and its implications. Theor. Comput. Sci., 348(2-3):357-365, 2005. URL: https://doi.org/10.1016/J.TCS.2005.09.023.
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