On stable flows and preflows

We propose a new algorithm of finding a stable flow in a network with several sources and sinks. It is based on the idea of preflows (applied in the 1970s for a faster solution of the classical maximal flow problem) and has time complexity $O(nm)$ for a network with $n$ vertices and $m$ edges. The obtained results are further generalized to a larger class of objects, the so-called stable quasi-flows with bounded deviations from the balanced relations in nonterminal vertices.