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. Strongly polynomial-time algorithms are only known for weighted general factor problems that are reducible to the weighted matching problem by gadget constructions. 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：一般因子是匹配的推广。给定图 $G$ 及其每个顶点 $v$ 上的可行度集合 $\pi(v)$（称为度约束），一般因子问题旨在寻找 $G$ 的一个（生成）子图 $F$，使得对 $G$ 中每个顶点 $v$ 有 $\text{deg}_F(x) \in \pi(v)$。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。加权一般因子问题是在边赋权图中寻找总权重最大的一般因子。目前，仅对于可通过构造 gadget 归约为加权匹配问题的加权一般因子问题，已知强多项式时间算法。本文提出了首个针对一类具有实值边权且经证明无法通过构造 gadget 归约为加权匹配问题的加权一般因子问题的强多项式时间算法。