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$G$，其每个顶点$v$关联一个可行度数集合$\pi(v)$（称为度数约束），一般因子问题是指寻找图$G$的一个（生成）子图$F$，使得对于$G$的每个顶点$v$，均有$\text{deg}_F(x) \in \pi(v)$。当所有度数约束均为对称$\Delta$-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指在边赋权图中寻找总权重最大的一般因子。目前，仅对于可通过构造技巧归约为加权匹配问题的加权一般因子问题，存在已知的强多项式时间算法。本文针对一类具有实数值边权重、且已被证明无法通过构造技巧归约为加权匹配问题的加权一般因子问题，提出了首个强多项式时间算法。