Theory and A Heuristic for the Minimum Path Flow Decomposition Problem

Shao, Mingfu; Kingsford, Carl

doi:10.1109/tcbb.2017.2779509

Cited by 26 publications

(41 citation statements)

References 37 publications

(46 reference statements)

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“…Many approximation algorithms have been developed for finding a minimum path flow decomposition, e.g. [40,41], but these algorithms could not even handle our smallest data set (a mixture of 2 haplotypes of length 2500 bp). Therefore, we resort to other, more efficient means for obtaining a set of haplotypes from the given flow solution [42].…”

Section: Greedy Path Extractionmentioning

confidence: 99%

Strain-aware assembly of genomes from mixed samples using flow variation graphs

Baaijens

Stougie

Schönhuth

2019

Preprint

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The goal of haplotype-aware genome assembly is to reconstruct all individual haplotypes from a mixed sample and to provide corresponding abundance estimates. We provide a referencegenome-independent solution based on the construction of a variation graph, capturing all diversity present in the sample. We solve the contig abundance estimation problem and propose a greedy algorithm to efficiently build maximal-length haplotypes. Finally, we obtain accurate frequency estimates for the reconstructed haplotypes through linear programming techniques. Our method outperforms state-of-the-art approaches on viral quasispecies benchmarks and has the potential to assemble bacterial genomes in a strain-aware manner as well.

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Section: Greedy Path Extractionmentioning

confidence: 99%

Strain-aware assembly of genomes from mixed samples using flow variation graphs

Baaijens

Stougie

Schönhuth

2019

Preprint

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“…Finding a flow decomposition with the minimum number of weighted paths is a well-studied problem in computer science. Even when restricted to DAGs, the minimum FD problem is NP-hard [11], and thus various practical approaches to it exist: approximation algorithms [12], [13], [14], [15], [16], [17], FPT algorithms [9], greedy algorithms [11], [18]. By taking the set of subpaths constraints to be empty (or to correspond to all edges of the graph with non-zero flow), it follows that also finding a solution to the FDSC problem with a minimum number of paths is NP-hard.…”

Section: Related Workmentioning

confidence: 99%

“…We implement both algorithms for FDSC, and perform a proof-of-concept study of their usefulness in RNA assembly. We experiment on a dataset developed by Shao et al [18] to study their heuristic for the minimum FD problem. The same dataset was then used by Kloster et al [9], who focused on studying the usefulness of standard minimum flow decompositions in RNA assembly, as explained above.…”

Section: Contributionsmentioning

confidence: 99%

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Flow Decomposition With Subpath Constraints

Williams

Tomescu

Mumey

2023

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Flow network decomposition is a natural model for problems where we are given a flow network arising from superimposing a set of weighted paths and would like to recover the underlying data, i.e., decompose the flow into the original paths and their weights. Thus, variations on flow decomposition are often used as subroutines in multiassembly problems such as RNA transcript assembly. In practice, we frequently have access to information beyond flow values in the form of subpaths, and many tools incorporate these heuristically. But despite acknowledging their utility in practice, previous work has not formally addressed the effect of subpath constraints on the accuracy of flow network decomposition approaches. We formalize the flow decomposition with subpath constraints problem, give the first algorithms for it, and study its usefulness for recovering ground truth decompositions. For finding a minimum decomposition, we propose both a heuristic and an FPT algorithm. Experiments on RNA transcript datasets show that for instances with larger solution path sets, the addition of subpath constraints finds 13% more ground truth solutions when minimal decompositions are found exactly, and 30% more ground truth solutions when minimal decompositions are found heuristically.

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“…StringTie [ 6 ] iteratively finds the heaviest path of a flow network constructed from splice graphs. A theoretical work by Shao et al [ 10 ] studies the minimum path decomposition of splice graphs when the edge abundances satisfy flow balance constraints. Better network flow estimation on splice graphs inspires improvement of transcriptome assembly methods.…”

Section: Introductionmentioning

confidence: 99%

Exact transcript quantification over splice graphs

Zheng

Kingsford

2021

Algorithms Mol Biol

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Background The probability of sequencing a set of RNA-seq reads can be directly modeled using the abundances of splice junctions in splice graphs instead of the abundances of a list of transcripts. We call this model graph quantification, which was first proposed by Bernard et al. (Bioinformatics 30:2447–55, 2014). The model can be viewed as a generalization of transcript expression quantification where every full path in the splice graph is a possible transcript. However, the previous graph quantification model assumes the length of single-end reads or paired-end fragments is fixed. Results We provide an improvement of this model to handle variable-length reads or fragments and incorporate bias correction. We prove that our model is equivalent to running a transcript quantifier with exactly the set of all compatible transcripts. The key to our method is constructing an extension of the splice graph based on Aho-Corasick automata. The proof of equivalence is based on a novel reparameterization of the read generation model of a state-of-art transcript quantification method. Conclusion We propose a new approach for graph quantification, which is useful for modeling scenarios where reference transcriptome is incomplete or not available and can be further used in transcriptome assembly or alternative splicing analysis.

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Theory and A Heuristic for the Minimum Path Flow Decomposition Problem

Cited by 26 publications

References 37 publications

Strain-aware assembly of genomes from mixed samples using flow variation graphs

Strain-aware assembly of genomes from mixed samples using flow variation graphs

Flow Decomposition With Subpath Constraints

Exact transcript quantification over splice graphs

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