Flow Decomposition with Subpath Constraints

Authors Lucia Williams , Alexandru I. Tomescu , Brendan Mumey

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Author Details

Lucia Williams
  • School of Computing, Montana State University, Bozeman, MT, USA
Alexandru I. Tomescu
  • Department of Computer Science, University of Helsinki, Finland
Brendan Mumey
  • School of Computing, Montana State University, Bozeman, MT, USA


Computational efforts were performed on the Hyalite High Performance Computing System, operated and supported by University Information Technology Research Cyberinfrastructure at Montana State University.

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Lucia Williams, Alexandru I. Tomescu, and Brendan Mumey. Flow Decomposition with Subpath Constraints. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Network flows
  • Applied computing → Computational transcriptomics
  • Flow decomposition
  • subpath constraints
  • RNA-Seq


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