We consider the problem of maximizing a non-negative submodular function under the $b$-matching constraint, in the semi-streaming model. When the function is linear, monotone, and non-monotone, we obtain the approximation ratios of $2+\varepsilon$, $3 + 2 \sqrt{2} \approx 5.828$, and $4 + 2 \sqrt{3} \approx 7.464$, respectively. We also consider a generalized problem, where a $k$-uniform hypergraph is given, along with an extra matroid constraint imposed on the edges, with the same goal of finding a $b$-matching that maximizes a submodular function. We extend our technique to this case to obtain an algorithm with an approximation of $\frac{8}{3}k+O(1)$.

翻译：我们考虑了在半流模式中最大限度地增加非负值子模块功能的问题。当函数为线性、单色和不单色时,我们得到的近似比率分别为2 ⁇ varepsilon$、3+2\sqrt{2}\ approx 5.828}和4+2\sqrt{3}\ approx 7.464$。我们还考虑到一个普遍的问题,即提供美元单色超标,同时对边缘实施超异机体约束,同样的目标是找到美元比值,使亚色函数最大化。我们将我们的技术推广到这个案例,以获得一种接近$\c{8}{{{{3}k+O(1)$的算法。