Flow Decomposition With Subpath Constraints

Williams, Lucia; Tomescu, Alexandru I.; Mumey, Brendan

doi:10.1109/tcbb.2022.3147697

Cited by 10 publications

(30 citation statements)

References 31 publications

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“…If errors are minimal, the weights on the edges should form a flow on the network, and the underlying sequences and their abundances must be some decomposition of the flow into weighted paths. For RNA assembly, recent work [22,59] has confirmed the common assertion (e.g., by [49,43,23,31,63,28,30]) that the true transcripts and abundances should be minimum flow decomposition. No such study has been done for viral quasispecies assembly, but existing tools seek minimum-sized decompositions [4,57].…”

Section: Minimum Flow Decomposition In Multiassemblymentioning

confidence: 79%

“…For example, many tools account for paired-end reads by requiring that they be included in the same path. Another common strategy is to incorporate longer reads as subpath constraints or phasing paths [38,43,59] which again must be covered by some predicted transcript (i.e. flow path).…”

Section: Our Contributionsmentioning

confidence: 99%

“…We compare InexactFlowILP with IFDSolver, which is an implementation of a heuristic algorithm for MIFD by [58]. Given the size of the datasets, we set a time limit for each graph, as also done by [22,59] (we use 1 minute in all cases, except that we also include a run of Toboggan with a 5 minute time limit). The runtimes of our ILP implementations include the linear scan in increasing order to find the smallest k for which there is a k-flow decomposition.…”

Section: Experiments Designmentioning

confidence: 99%

See 2 more Smart Citations

Fast, Flexible, and Exact Minimum Flow Decompositions via ILP

Dias,

Williams,

Mumey

et al. 2022

Preprint

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Minimum flow decomposition (MFD) -the problem of finding a minimum set of paths that perfectly decomposes a flow -is a classical problem in Computer Science, and variants of it are powerful models in multiassembly problems in Bioinformatics (e.g. RNA assembly). However, because this problem and its variants are NP-hard, practical multiassembly tools either use heuristics or solve simpler, polynomial-time solvable versions of the problem, which may yield solutions that are not minimal or do not perfectly decompose the flow. Many RNA assemblers also use integer linear programming (ILP) formulations of such practical variants, having the major limitation they need to encode all the potentially exponentially many solution paths. Moreover, the only exact solver for MFD does not scale to large instances, and cannot be efficiently generalized to practical MFD variants.In this work, we provide the first practical ILP formulation for MFD (and thus the first fast and exact solver for MFD), based on encoding all of the exponentially many solution paths using only a quadratic number of variables. On both simulated and real flow graphs, our approach solves any instance in under 13 seconds. We also show that our ILP formulation can be easily and efficiently adapted for many practical variants, such as incorporating longer or paired-end reads, or minimizing flow errors.We hope that our results can remove the current tradeoff between the complexity of a multiassembly model and its tractability, and can lie at the core of future practical RNA assembly tools. Our implementations are freely available at github.com/algbio/MFD-ILP.

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Section: Minimum Flow Decomposition In Multiassemblymentioning

confidence: 79%

Section: Our Contributionsmentioning

confidence: 99%

Section: Experiments Designmentioning

confidence: 99%

See 1 more Smart Citation

Fast, Flexible, and Exact Minimum Flow Decompositions via ILP

Dias,

Williams,

Mumey

et al. 2022

Preprint

Self Cite

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“…In both cases, the weighted transcripts are superimposed to build splice graphs as described above. This dataset has also been used in other flow decomposition benchmarking studies [26,57]. There are 17,335,407 graphs in total in this dataset, of which 8,301,682 are non-trivial (47.89%).…”

Section: Catfish Datasetmentioning

confidence: 99%

“…If there are multiple optimal flow decomposition solutions, then the reconstructed sequences may not match the original ones, and thus be incorrect. While many popular multiassembly tools look for minimum flow decompositions, Williams et al [57] analyzed an error-free transcript dataset to find that 20% of human genes admit multiple minimum flow decomposition solutions.…”

Section: Introductionmentioning

confidence: 99%

Safety and Completeness in Flow Decompositions for RNA Assembly

Khan¹,

Kortelainen²,

Cáceres³

et al. 2022

Preprint

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Decomposing a network flow into weighted paths is a problem with numerous applications, ranging from networking, transportation planning to bioinformatics. In some applications we look for any decomposition that is optimal with respect to some property, such as number of paths used, robustness to edge deletion, or length of the longest path. However, in many bioinformatic applications, we seek a specific decomposition where the paths correspond to some underlying data that generated the flow. For realistic inputs, no optimization criteria can be guaranteed to uniquely identify the correct decomposition. Therefore, we propose to instead report the safe paths, which are subpaths of at least one path in every flow decomposition.Recently, Ma, Zheng, and Kingsford [WABI 2020] addressed the existence of multiple optimal solutions in a probabilistic framework, which is referred to as non-identifiability. In a follow-up work [RECOMB 2021], they gave a quadratic-time algorithm based on a global criterion for solving a problem called AND-Quant, which generalizes the problem of reporting whether a given path is safe.In this work, we give the first local characterization of safe paths for flow decompositions in directed acyclic graphs (DAGs), leading to a practical algorithm for finding the complete set of safe paths. We additionally evaluated our algorithms against the trivial safe algorithms (unitigs, extended unitigs) and the popularly used heuristic (greedy-width) for flow decomposition on RNA transcripts datasets. We find that despite maintaining perfect precision the safe and complete algorithm reports significantly higher coverage (≈50% more) as compared to trivial safe algorithms. The greedy-width algorithm though reporting a better coverage, reports significantly lower precision on complex graphs (for genes expressing a large number of transcripts). Overall, our safe and complete algorithm outperforms (by ≈20%) greedy-width on a unified metric (F-Score) considering both coverage and precision when the evaluated dataset has significant number of complex graphs. Moreover, it also has superior time (3−5×) and space efficiency (1.2−2.2×), resulting in a better and more practical approach for bioinformatics applications of flow decomposition.

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Improving RNA Assembly via Safety and Completeness in Flow Decompositions

Khan

Kortelainen

Cáceres

et al. 2022

Journal of Computational Biology

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Decomposing a network flow into weighted paths is a problem with numerous applications, ranging from networking, transportation planning, to bioinformatics. In some applications we look for a decomposition that is optimal with respect to some property, such as the number of paths used, robustness to edge deletion, or length of the longest path. However, in many bioinformatic applications, we seek a specific decomposition where the paths correspond to some underlying data that generated the flow. In these cases, no optimization criteria guarantee the identification of the correct decomposition. Therefore, we propose to instead report the safe paths, which are subpaths of at least one path in every flow decomposition. In this work, we give the first local characterization of safe paths for flow decompositions in directed acyclic graphs, leading to a practical algorithm for finding the complete set of safe paths. In addition, we evaluate our algorithm on RNA transcript data sets against a trivial safe algorithm (extended unitigs), the recently proposed safe paths for path covers (TCBB 2021) and the popular heuristic greedy-width . On the one hand, we found that besides maintaining perfect precision, our safe and complete algorithm reports a significantly higher coverage ( 50 more) compared with the other safe algorithms. On the other hand, the greedy-width algorithm although reporting a better coverage, it also reports a significantly lower precision on complex graphs (for genes expressing a large number of transcripts). Overall, our safe and complete algorithm outperforms (by 20 ) greedy-width on a unified metric (F-score) considering both coverage and precision when the evaluated data set has a significant number of complex graphs. Moreover, it also has a superior time ( 5 ) and space performance ( 2 2 2 ), resulting in a better and more practical approach for bioinformatic applications of flow decomposition.

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Flow Decomposition With Subpath Constraints

Cited by 10 publications

References 31 publications

Fast, Flexible, and Exact Minimum Flow Decompositions via ILP

Fast, Flexible, and Exact Minimum Flow Decompositions via ILP

Safety and Completeness in Flow Decompositions for RNA Assembly

Improving RNA Assembly via Safety and Completeness in Flow Decompositions

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