General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$ such that $\text{deg}_F(x) \in \pi(v)$ for every $v$ of $G$. When all degree constraints are symmetric $\Delta$-matroids, the problem is solvable in polynomial time. The weighted general factor problem is to find a general factor of the maximum total weight in an edge-weighted graph. In this paper, we present the first strongly polynomial-time algorithm for a type of weighted general factor problems with real-valued edge weights that is provably not reducible to the weighted matching problem by gadget constructions.

翻译：广义因子是匹配问题的推广。给定图$G$及其每个顶点$v$对应的可行度集合$\pi(v)$（称为度约束），广义因子问题旨在寻找$G$的一个（支撑）子图$F$，使得对$G$中每个顶点$v$满足$\text{deg}_F(x) \in \pi(v)$。当所有度约束均为对称$\Delta$-拟阵时，该问题可在多项式时间内求解。加权广义因子问题则要求在边赋权图中寻找总权值最大的广义因子。本文针对一类具有实值边权重的加权广义因子问题，提出了首个强多项式时间算法，该类问题已被证明无法通过构件构造归约为加权匹配问题。