An Approximation Algorithm for Multiroute Flow Decomposition

Suppakitpaisarn, Vorapong

doi:10.1016/j.endm.2016.03.048

Cited by 5 publications

(4 citation statements)

References 6 publications

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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%

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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Section: Related Workmentioning

confidence: 99%

Flow Decomposition With Subpath Constraints

Williams

Tomescu

Mumey

2023

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

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“…Finding the decomposition with the minimum number of paths and possibly cycles (or minimum flow decomposition ) is NP-hard, even if the flow network is a DAG (Vatinlen et al, 2008 ). On the theoretical side, this hardness result led to research on approximation algorithms (Baier et al, 2005 ; Baier et al, 2002 ; Hartman et al, 2012 ; Mumey et al, 2015 ; Suppakitpaisarn, 2016 ; Pieńkosz and Kołtyś, 2015 ) and FPT algorithms (Kloster et al, 2018 ). On the practical side, many approaches usually use a standard greedy-width heuristic (Vatinlen et al, 2008 ), of repeatedly removing an s – t path carrying the most amount of flow.…”

Section: Introductionmentioning

confidence: 99%

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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“…Finding the decomposition with the minimum number of paths and possibly cycles (or minimum flow decomposition) is NP-hard, even if the flow network is a DAG [53]. On the theoretical side, this hardness result led to research on approximation algorithms [21,48,43,36,6,7], and FPT algorithms [26]. On the practical side, many approaches usually employ a standard greedy-width heuristic [53], of repeatedly removing an s-t path carrying the most amount of flow.…”

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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An Approximation Algorithm for Multiroute Flow Decomposition

Cited by 5 publications

References 6 publications

Flow Decomposition With Subpath Constraints

Flow Decomposition With Subpath Constraints

Improving RNA Assembly via Safety and Completeness in Flow Decompositions

Safety and Completeness in Flow Decompositions for RNA Assembly

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