We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximize the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from a given finite set. Our method is based on a novel factorization theorem for finite semigroups that, applied to a suitable flow semigroup, allows to derive small witnesses. This generalizes to multiple in/output vertices, as well as regular constraints.

翻译：我们提出了一种新的代数技术，用于在多项式空间内解决序列流问题。该任务旨在最大化通过图的流量，其中边容量可以通过从给定有限集合中选择容量标记序列随时间改变。我们的方法基于有限半群的一个新颖分解定理，该定理应用于合适的流半群，能够推导出小型见证。该方法可推广至多个输入/输出顶点以及正则约束。