Fast, Flexible, and Exact Minimum Flow Decompositions via ILP

Dias, Fernando H. C.; Williams, Lucia; Mumey, Brendan; Tomescu, Alexandru I.

doi:10.1007/978-3-031-04749-7_14

Cited by 6 publications

(23 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, it is known that if one is also given a set of paths that must appear as subpath in at least one solution path (subpath constraints, arising from long reads aligned to the graph), then the accuracy further increases [29]. Such subpath constraints have been added on top of the ILP formulation for MFD, see [8]. They can also be trivially added to our ILP from Section 3 by analogously requiring that they appear as subpaths also in our solution paths.…”

Section: Discussionmentioning

confidence: 99%

“…We denote the bounded-error formulation (Problem 2) as Bounded; the inexact formulation (Problem 3) as Inexact; the least-squares formulation (Problem 4) as LeastSquares; the minimum path error formulation (Problem 5) as MinPathError. We also run the ILP formulation from [8] (Problem 1), which we denote as MFD. Our implementations were done using the GUROBI Python API under default settings.…”

Section: Solversmentioning

confidence: 99%

“…Also, efficient heuristics [26, 20], or a fixed-parameter tractable algorithm (in the size of the MFD) [13] exist. Recently, it was shown that there exists an Integer Linear Programming (ILP) formulation for MFD [8], which is the fastest practical and exact solution to the problem to date.…”

Section: Introductionmentioning

confidence: 99%

“…For the latter problem, one can compute a “good flow” falling inside the edge intervals and then heuristically decompose this flow. Recently, exact and efficient ILP-based solutions for both problems were shown to exist [8].…”

Section: Introductionmentioning

confidence: 99%

“…Even though practical tools may include additional information to the problem statements (e.g., long reads, as in [31], or pre-assembled contigs as in [2, 18]), models similar to least-squares and inexact flow have been central for dealing with weights not forming perfect flows. In this paper, for the first time, we experimentally evaluate the accuracy of exact solutions to the least-squares and minimum inexact flow decomposition models by implementing the exact ILP-based solutions from [8]. On a version of the dataset of [20] where we add errors, we show that the former model reaches an accuracy of 68–80% (depending on how stringent the evaluation metric is and how erroneous the edge weights are), while the latter one reaches an accuracy of 81–91%.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Accurate Flow Decomposition via Robust Integer Linear Programming

Dias

Tomescu

2023

Preprint

Self Cite

View full text Add to dashboard Cite

Minimum flow decomposition (MFD) is a common problem across various fields of Computer Science, where a flow is decomposed into a minimum set of weighted paths. However, in Bioinformatics applications, such as RNA transcript or quasi-species assembly, the flow is erroneous, since is obtained from noisy read coverages. Typical generalizations of the MFD problem to handle errors are based on least-squares formulations, or on modeling the erroneous flow values as ranges. All of these are thus focused on error-handling at the level of individual edges. Interpreting the flow decomposition problem as a robust optimization problem, we lift error-handling from individual edges to solution paths. As such, we introduce a new minimum path-error flow decomposition problem, for which we give an efficient Integer Linear Programming formulation. Our experimental results reveal that our formulation can account for errors with an accuracy significantly surpassing that of previous error-handling formulations, with computational requirements that remain practical.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Solversmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Accurate Flow Decomposition via Robust Integer Linear Programming

Dias

Tomescu

2023

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Fast, Flexible, and Exact Minimum Flow Decompositions via ILP

Dias

Williams²,

Mumey³

et al. 2022

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Efficient Minimum Flow Decomposition via Integer Linear Programming

Dias

Williams

Mumey

et al. 2022

Journal of Computational Biology

Self Cite

View full text Add to dashboard Cite

Minimum flow decomposition (MFD) is an NP-hard problem asking to decompose a network flow into a minimum set of paths (together with associated weights). Variants of it are powerful models in multiassembly problems in Bioinformatics, such as RNA assembly. Owing to its hardness, 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. Here, we provide the first fast and exact solver for MFD on acyclic flow networks, based on Integer Linear Programming (ILP). Key to our approach is an encoding of all the exponentially many solution paths using only a quadratic number of variables. We also extend our ILP formulation to many practical variants, such as incorporating longer or paired-end reads, or minimizing flow errors. On both simulated and real-flow splicing graphs, our approach solves any instance in <13 seconds. We hope that our formulations can lie at the core of future practical RNA assembly tools. Our implementations are freely available on Github.

show abstract

Fast, Flexible, and Exact Minimum Flow Decompositions via ILP

Cited by 6 publications

References 52 publications

Accurate Flow Decomposition via Robust Integer Linear Programming

Accurate Flow Decomposition via Robust Integer Linear Programming

Fast, Flexible, and Exact Minimum Flow Decompositions via ILP

Efficient Minimum Flow Decomposition via Integer Linear Programming

Contact Info

Product

Resources

About