  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.
