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Producing Genomic Sequences after Genome Scaffolding with Ambiguous Paths: Complexity, Approximation and Lower Bounds

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Abstract

Scaffolding is the final step in assembling Next Generation Sequencing data, in which pre-assembled contiguous regions (”contigs”) are oriented and ordered using information that links them (for example, mapping of paired-end reads). As the genome of some species is highly repetitive, we allow placing some contigs multiple times, thereby generalizing established computational models for this problem. We study the subsequent problems induced by the translation of solutions of the model back to actual sequences, proposing models and analyzing the complexity of the resulting computational problems. We find both polynomial-time and \(\mathcal {NP}\)-hard special cases like planarity or bounded degree. Finally, we propose two polynomial-time approximation algorithms according to cut/weight score.

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Notes

  1. Solution graphs differ from scaffold graphs in that the multiplicity function is defined on all edges and not just on matching edges.

  2. A sequences is called chimeric if it does not occur in the target genome, but is made up of chunks picked from different chromosomes or regions of the genome.

  3. N50 is a statistical measure on contig lengths: given a set of contigs, the N50 is defined as the sequence length of the shortest contig at 50% of the total genome length.

  4. A graph is co-bipartite if its vertices can be partitioned into two cliques.

  5. The (widely believed) “Exponential Time Hypothesis” (ETH) states that the boolean satisfyability problem (SAT) cannot be solved in \(2^{o(n)}\) time, where n is the number of variables of the input formula.

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Acknowledgements

This work was partially supported by the Région Occitanie.

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Authors and Affiliations

  1. LIRMM - CNRS UMR, 5506, Montpellier, France

    Tom Davot, Annie Chateau & Rodolphe Giroudeau

  2. CNRS, LIGM, Paris, France

    Mathias Weller

  3. MIPS EA, 2332, Mulhouse, France

    Dorine Tabary

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  1. Tom Davot
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  2. Annie Chateau
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  3. Rodolphe Giroudeau
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  4. Mathias Weller
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  5. Dorine Tabary
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Correspondence to Tom Davot.

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Davot, T., Chateau, A., Giroudeau, R. et al. Producing Genomic Sequences after Genome Scaffolding with Ambiguous Paths: Complexity, Approximation and Lower Bounds. Algorithmica 83, 2063–2095 (2021). https://doi.org/10.1007/s00453-021-00819-6

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