Space Efficient Merging of de Bruijn Graphs and Wheeler Graphs

The merging of succinct data structures is a well established technique for the space efficient construction of large succinct indexes. In the first part of the paper we propose a new algorithm for merging succinct representations of de Bruijn graphs . Our algorithm has the same asymptotic cost of t...

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Published in:	Algorithmica Vol. 84; no. 3; pp. 639 - 669
Main Authors:	Egidi, Lavinia, Louza, Felipe A., Manzini, Giovanni
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.03.2022 Springer Nature B.V
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Asymptotic properties Computer Science Computer Systems Organization and Communication Networks Data structures Data Structures and Information Theory Graph theory Graphical representations Graphs Mathematics of Computing Special Issue from London Stringology Days & London Algorithmic Workshop Theory of Computation Succinct data structures Space efficient algorithms de Bruijn graphs Wheeler graphs BWT variants
ISSN:	0178-4617, 1432-0541
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Abstract	The merging of succinct data structures is a well established technique for the space efficient construction of large succinct indexes. In the first part of the paper we propose a new algorithm for merging succinct representations of de Bruijn graphs . Our algorithm has the same asymptotic cost of the state of the art algorithm for the same problem but it uses less than half of its working space. A novel important feature of our algorithm, not found in any of the existing tools, is that it can compute the Variable Order succinct representation of the union graph within the same asymptotic time/space bounds. In the second part of the paper we consider the more general problem of merging succinct representations of Wheeler graphs , a recently introduced graph family which includes as special cases de Bruijn graphs and many other known succinct indexes based on the BWT or one of its variants. In this paper we provide a space efficient algorithm for Wheeler graph merging; our algorithm works under the assumption that the union of the input Wheeler graphs has an ordering that satisfies the Wheeler conditions and which is compatible with the ordering of the original graphs.
AbstractList	The merging of succinct data structures is a well established technique for the space efficient construction of large succinct indexes. In the first part of the paper we propose a new algorithm for merging succinct representations of de Bruijn graphs. Our algorithm has the same asymptotic cost of the state of the art algorithm for the same problem but it uses less than half of its working space. A novel important feature of our algorithm, not found in any of the existing tools, is that it can compute the Variable Order succinct representation of the union graph within the same asymptotic time/space bounds. In the second part of the paper we consider the more general problem of merging succinct representations of Wheeler graphs, a recently introduced graph family which includes as special cases de Bruijn graphs and many other known succinct indexes based on the BWT or one of its variants. In this paper we provide a space efficient algorithm for Wheeler graph merging; our algorithm works under the assumption that the union of the input Wheeler graphs has an ordering that satisfies the Wheeler conditions and which is compatible with the ordering of the original graphs. The merging of succinct data structures is a well established technique for the space efficient construction of large succinct indexes. In the first part of the paper we propose a new algorithm for merging succinct representations of de Bruijn graphs . Our algorithm has the same asymptotic cost of the state of the art algorithm for the same problem but it uses less than half of its working space. A novel important feature of our algorithm, not found in any of the existing tools, is that it can compute the Variable Order succinct representation of the union graph within the same asymptotic time/space bounds. In the second part of the paper we consider the more general problem of merging succinct representations of Wheeler graphs , a recently introduced graph family which includes as special cases de Bruijn graphs and many other known succinct indexes based on the BWT or one of its variants. In this paper we provide a space efficient algorithm for Wheeler graph merging; our algorithm works under the assumption that the union of the input Wheeler graphs has an ordering that satisfies the Wheeler conditions and which is compatible with the ordering of the original graphs.
Author	Louza, Felipe A. Manzini, Giovanni Egidi, Lavinia
Author_xml	– sequence: 1 givenname: Lavinia surname: Egidi fullname: Egidi, Lavinia organization: University of Eastern Piedmont – sequence: 2 givenname: Felipe A. orcidid: 0000-0003-2931-1470 surname: Louza fullname: Louza, Felipe A. email: louza@ufu.br organization: Federal University of Uberlândia – sequence: 3 givenname: Giovanni surname: Manzini fullname: Manzini, Giovanni organization: University of Pisa
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Cites_doi	10.1007/s00453-011-9535-0 10.1093/bioinformatics/btx067 10.1007/s11786-016-0281-1 10.1145/2649387.2649431 10.1145/1290672.1290680 10.1007/978-3-642-33122-0_18 10.1093/bioinformatics/btu014 10.1142/S0129054118430037 10.1137/1.9781611975994.55 10.1007/978-3-319-67428-5_15 10.1016/j.tcs.2019.11.001 10.1145/1240233.1240243 10.1093/bioinformatics/btu756 10.1093/bioinformatics/btu584 10.1093/bioinformatics/btz350 10.1109/DCC.2019.00020 10.1016/j.tcs.2017.06.016 10.1038/ng.1028 10.1016/j.tcs.2017.02.020 10.1109/DCC.2016.17 10.1101/138016 10.1186/s13015-019-0140-0 10.1016/j.tcs.2007.07.014 10.1137/1.9781611974768.2 10.1137/1.9781611976465.153 10.1007/978-3-030-32686-9_24 10.1109/DCC.2015.70 10.1016/0020-0190(79)90002-4 10.1073/pnas.171285098 10.1186/1748-7188-8-22 10.1007/978-3-030-00479-8_1 10.1145/1082036.1082039 10.1145/1868237.1868248 10.1109/DCC.2019.00022 10.1145/1613676.1613680
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ACM (2014) IqbalZCaccamoMTurnerIFlicekPMcVeanGDe novo assembly and genotyping of variants using colored de Bruijn graphsNat. Genet.201244222623210.1038/ng.1028 Egidi, L., Louza, F.A., Manzini, G.: Space-efficient merging of succinct de Bruijn graphs. In: SPIRE. LNCS, vol. 11811, pp. 337–351. Springer (2019) MuggliMDAlipanahiBBoucherCBuilding large updatable colored de Bruijn graphs via mergingBioinformatics20193514i51i6010.1093/bioinformatics/btz350 Ferragina, P., Gagie, T., Manzini, G.: Lightweight data indexing and compression in external memory. Algorithmica (2011) GagieTManziniGSirénJWheeler graphs: A framework for bwt-based data structuresTheor. Comput. Sci.20176986778371936410.1016/j.tcs.2017.06.016 Egidi, L., Louza, F.A., Manzini, G., Telles, G.P.: External memory BWT and LCP computation for sequence collections with applications. In: WABI. LIPIcs, vol. 113, pp. 10:1–10:14. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2018) AspvallBPlassMFTarjanREA linear-time algorithm for testing the truth of certain quantified boolean formulasInf. Process. Lett.19798312112352645110.1016/0020-0190(79)90002-4 Bowe, A., Onodera, T., Sadakane, K., Shibuya, T.: Succinct de Bruijn graphs. In: WABI. LNCS, vol. 7534, pp. 225–235. Springer, Berlin (2012) Gagie, T., Gourdel, G., Manzini, G.: Compressing and indexing aligned readsets. In: WABI. LIPIcs, vol. 201. pp. 13:1–13:21, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2021) EgidiLLouzaFAManziniGTellesGPExternal memory BWT and LCP computation for sequence collections with applicationsAlgorith. Mol. Biol.20191416:16:1510.1186/s13015-019-0140-0 FerraginaPVenturiniRThe compressed permuterm indexACM Trans. Algori.20107110:110:21274712710.1145/1868237.1868248 Sirén, J.: Indexing variation graphs. In: ALENEX. pp. 13–27. 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Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019) DurbinREfficient haplotype matching and storage using the positional Burrows-Wheeler transform (PBWT)Bioinformatics20143091266127210.1093/bioinformatics/btu014 Alanko, J., D’Agostino, G., Policriti, A., Prezza, N.: Regular languages meet prefix sorting. In: SODA. pp. 911–930. SIAM (2020) ChikhiRRizkGSpace-efficient and exact de Bruijn graph representation based on a bloom filterAlgorith. Mol. Biol.201382210.1186/1748-7188-8-22 Boucher, C., Bowe, A., Gagie, T., Puglisi, S.J., Sadakane, K.: Variable-order de Bruijn graphs. In: DCC. pp. 383–392. IEEE (2015) Alipanahi, B., Kuhnle, A., Boucher, C.: Recoloring the colored de Bruijn graph. In: SPIRE. LNCS, vol. 11147, pp. 1–11. Springer (2018) EgidiLManziniGLightweight merging of compressed indices based on BWT variantsTheor. Comput. 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Algorithms 3(4) (2007) NaJCKimHMinSParkHLecroqTLéonardMMouchardLParkKFM-index of alignment with gapsTheor. Comput. Sci.2018710148157375861010.1016/j.tcs.2017.02.020 BelazzouguiDNavarroGOptimal lower and upper bounds for representing sequencesACM T. Algorithms201511431:131:2133612161398.68103 855_CR22 MD Muggli (855_CR38) 2017; 33 855_CR43 D Belazzougui (855_CR10) 2018; 29 855_CR20 855_CR42 855_CR41 R Chikhi (855_CR14) 2013; 8 P Ferragina (855_CR26) 2010; 7 S Marcus (855_CR35) 2014; 30 T Gagie (855_CR28) 2017; 698 855_CR29 P Ferragina (855_CR23) 2005; 52 855_CR27 855_CR25 855_CR24 R Durbin (855_CR16) 2014; 30 855_CR2 855_CR3 855_CR4 855_CR5 855_CR1 855_CR12 L Egidi (855_CR19) 2019; 14 855_CR11 855_CR30 855_CR7 JC Na (855_CR39) 2018; 710 855_CR9 855_CR18 855_CR17 J Kärkkäinen (855_CR33) 2017; 11 L Egidi (855_CR21) 2020; 812 855_CR15 855_CR37 855_CR13 MD Muggli (855_CR36) 2019; 35 S Mantaci (855_CR34) 2007; 387 J Holt (855_CR31) 2014; 30 Z Iqbal (855_CR32) 2012; 44 B Aspvall (855_CR6) 1979; 8 D Belazzougui (855_CR8) 2015; 11 PA Pevzner (855_CR40) 2001; 98
References_xml	– reference: BelazzouguiDNavarroGOptimal lower and upper bounds for representing sequencesACM T. Algorithms201511431:131:2133612161398.68103 – reference: FerraginaPVenturiniRThe compressed permuterm indexACM Trans. Algori.20107110:110:21274712710.1145/1868237.1868248 – reference: Alipanahi, B., Kuhnle, A., Boucher, C.: Recoloring the colored de Bruijn graph. In: SPIRE. LNCS, vol. 11147, pp. 1–11. Springer (2018) – reference: Ferragina, P., Manzini, G., Mäkinen, V., Navarro, G.: Compressed representations of sequences and full-text indexes. ACM Trans. Algorithms 3(2), 20 (2007) – reference: Cotumaccio, N., Prezza, N.: On indexing and compressing finite automata. In: SODA. SIAM (2021) – reference: PevznerPATangHWatermanMSAn eulerian path approach to dna fragment assemblyProc. Natl. Acad. Sci.2001981797489753185528710.1073/pnas.171285098 – reference: AspvallBPlassMFTarjanREA linear-time algorithm for testing the truth of certain quantified boolean formulasInf. Process. Lett.19798312112352645110.1016/0020-0190(79)90002-4 – reference: MarcusSLeeHSchatzMCSplitmem: a graphical algorithm for pan-genome analysis with suffix skipsBioinformatics201430243476348310.1093/bioinformatics/btu756 – reference: MuggliMDAlipanahiBBoucherCBuilding large updatable colored de Bruijn graphs via mergingBioinformatics20193514i51i6010.1093/bioinformatics/btz350 – reference: Belazzougui, D., Cunial, F.: Fully-functional bidirectional Burrows-Wheeler indexes and infinite-order de Bruijn graphs. In: CPM. LIPIcs, vol. 128, pp. 10:1–10:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019) – reference: Alanko, J., D’Agostino, G., Policriti, A., Prezza, N.: Wheeler languages. CoRR 2002.10303 (2020). https://arxiv.org/abs/2002.10303 – reference: Bowe, A., Onodera, T., Sadakane, K., Shibuya, T.: Succinct de Bruijn graphs. In: WABI. LNCS, vol. 7534, pp. 225–235. Springer, Berlin (2012) – reference: Baier, U., Dede, K.: BWT tunnel planning is hard but manageable. In: DCC. pp. 142–151. IEEE (2019) – reference: Boucher, C., Bowe, A., Gagie, T., Puglisi, S.J., Sadakane, K.: Variable-order de Bruijn graphs. In: DCC. pp. 383–392. IEEE (2015) – reference: Gagie, T., Gourdel, G., Manzini, G.: Compressing and indexing aligned readsets. In: WABI. LIPIcs, vol. 201. pp. 13:1–13:21, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2021) – reference: Ferragina, P., Gagie, T., Manzini, G.: Lightweight data indexing and compression in external memory. Algorithmica (2011) – reference: Sirén, J.: Indexing variation graphs. In: ALENEX. pp. 13–27. SIAM (2017) – reference: Egidi, L., Louza, F.A., Manzini, G., Telles, G.P.: External memory BWT and LCP computation for sequence collections with applications. In: WABI. LIPIcs, vol. 113, pp. 10:1–10:14. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2018) – reference: EgidiLLouzaFAManziniGTellesGPExternal memory BWT and LCP computation for sequence collections with applicationsAlgorith. Mol. 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Snippet	The merging of succinct data structures is a well established technique for the space efficient construction of large succinct indexes. In the first part of...
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SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Asymptotic properties Computer Science Computer Systems Organization and Communication Networks Data structures Data Structures and Information Theory Graph theory Graphical representations Graphs Mathematics of Computing Special Issue from London Stringology Days & London Algorithmic Workshop Theory of Computation
Title	Space Efficient Merging of de Bruijn Graphs and Wheeler Graphs
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