The research behind our technology.
Flowty builds on algorithmic advances in multi-commodity flow, column generation, and resource-constrained shortest paths. Below are summaries of recent papers that inform the core solver stack.
ArXiv highlights
Two recent papers describe our approaches to large-scale multi-commodity flow and high-performance resource-constrained shortest paths.
Tree-based formulation for the multi-commodity flow problem
arXiv:2509.24656
Problem
Minimum-cost multi-commodity flow on large, capacitated networks.
Approach
Decompose a source-based formulation by representing flows as convex combinations of trees rooted at sources, and solve via column generation. The master problem has demand constraints that scale with the number of sources, not commodities.
Results
The paper reports order-of-magnitude speedups over direct LP solving and improved scalability compared to path-based formulations, solving instances with millions of commodities and hundreds of thousands of nodes.
Parallel pull labelling for the resource-constrained shortest path problem
arXiv:2511.01397
Problem
Resource constrained shortest path problems inside large-scale routing and pricing pipelines.
Approach
A pull labelling algorithm with bucket-level parallelism, bi-directional search with dynamic midpoint selection, and vectorized dominance checks.
Results
The paper reports speedups of roughly 14x on hard instances and up to 200x on the hardest cases, improving column generation performance.
Acquisition inquiries
Flowty's algorithms, solvers, and surrounding IP are available for acquisition. Get in touch to discuss.
Try the solver: docs.flowty.ai
CVR 39946408