The single-source unsplittable flow problem deals with a graph $G$, source single source $s$ and $k$ terminals for $k$ commodities. We want to find a flow such that each commodity is routed along exactly one path. I will be presenting the main algorithm that shows how to get an unsplittable flow such that the flow across an edge is violated by at most the maximum demand, assuming a feasible flow exists. In graphs which satisfy that the maximum demand is less than the minimum capacity and a feasible flow exists, we will see how to get a flow of congestion at most 2, that all demands can be satisfied as a union of 5 unsplittable flows and that 22.6% of the total demand can be satisfied unsplittably.
Based on the following paper: https://link.springer.com/article/10.1007/s004930050043
