Accelerating ILP Solvers for Minimum Flow Decompositions Through Search Space and Dimensionality Reductions

Authors Andreas Grigorjew , Fernando H. C. Dias , Andrea Cracco , Romeo Rizzi , Alexandru I. Tomescu

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Author Details

Andreas Grigorjew
  • University of Helsinki, Finland
Fernando H. C. Dias
  • Aalto University, Espoo, Finland
Andrea Cracco
  • University of Verona, Italy
Romeo Rizzi
  • University of Verona, Italy
Alexandru I. Tomescu
  • University of Helsinki, Finland


We are very grateful to Manuel Cáceres for a very helpful discussion on sets of independent safe paths.

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Andreas Grigorjew, Fernando H. C. Dias, Andrea Cracco, Romeo Rizzi, and Alexandru I. Tomescu. Accelerating ILP Solvers for Minimum Flow Decompositions Through Search Space and Dimensionality Reductions. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Given a flow network, the Minimum Flow Decomposition (MFD) problem is finding the smallest possible set of weighted paths whose superposition equals the flow. It is a classical, strongly NP-hard problem that is proven to be useful in RNA transcript assembly and applications outside of Bioinformatics. We improve an existing ILP (Integer Linear Programming) model by Dias et al. [RECOMB 2022] for DAGs by decreasing the solver’s search space using solution safety and several other optimizations. This results in a significant speedup compared to the original ILP, of up to 34× on average on the hardest instances. Moreover, we show that our optimizations apply also to MFD problem variants, resulting in speedups that go up to 219× on the hardest instances. We also developed an ILP model of reduced dimensionality for an MFD variant in which the solution path weights are restricted to a given set. This model can find an optimal MFD solution for most instances, and overall, its accuracy significantly outperforms that of previous greedy algorithms while being up to an order of magnitude faster than our optimized ILP.

Subject Classification

ACM Subject Classification
  • Theory of computation → Network flows
  • Applied computing → Bioinformatics
  • Flow decomposition
  • Integer Linear Programming
  • Safety
  • RNA-seq
  • RNA transcript assembly
  • isoform


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