Accelerating ILP solvers for Minimum Flow Decompositions through search space and dimensionality reductions
Year: 2023
Type: preprint
Abstract: 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 55-90x on average on the hardest instances. Moreover, we show that our optimizations apply also to MFD problem variants, resulting in similar speedups, going up to 123x 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.
Source: arXiv (Cornell University)
Institutions: University of Helsinki, Aalto University, University of Verona
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: European Commission, Academy of Finland
OpenAlex ID: W4388843610