We deepen the link between two classic areas of combinatorial optimization: augmentation and packing arborescences. We consider the following type of questions: What is the minimum number of arcs to be added to a digraph so that in the resulting digraph there exists some special kind of packing of arborescences? We answer this question for two problems: $h$-regular \textsf{M}-independent-rooted $(f,g)$-bounded $(\alpha, \beta)$-limited packing of mixed hyperarborescences and $h$-regular $(\ell, \ell')$-bordered $(\alpha, \beta)$-limited packing of $k$ hyperbranchings. We also solve the undirected counterpart of the latter, that is the augmentation problem for $h$-regular $(\ell, \ell')$-bordered $(\alpha, \beta)$-limited packing of $k$ rooted hyperforests. Our results provide a common generalization of a great number of previous results.

翻译：我们深化了组合优化中两个经典领域——增强与树形图填充——之间的联系。我们探讨以下类型的问题：需要向有向图中添加最少多少条弧，才能使得在生成的有向图中存在某种特殊的树形图填充？我们针对两个问题给出了答案：$h$-正则 \textsf{M}-独立根 $(f,g)$-有界 $(\alpha, \beta)$-受限混合超树形图填充，以及 $h$-正则 $(\ell, \ell')$-边界 $(\alpha, \beta)$-受限 $k$ 个超分支的填充。我们还解决了后者的无向对应问题，即 $h$-正则 $(\ell, \ell')$-边界 $(\alpha, \beta)$-受限 $k$ 个有根超森林填充的增强问题。我们的结果为大量先前的研究成果提供了一个共同的推广。