We study the store-and-forward packet routing problem for simultaneous multicasts, in which multiple packets have to be forwarded along given trees as fast as possible. This is a natural generalization of the seminal work of Leighton, Maggs and Rao, which solved this problem for unicasts, i.e. the case where all trees are paths. They showed the existence of asymptotically optimal $O(C + D)$-length schedules, where the congestion $C$ is the maximum number of packets sent over an edge and the dilation $D$ is the maximum depth of a tree. This improves over the trivial $O(CD)$ length schedules. We prove a lower bound for multicasts, which shows that there do not always exist schedules of non-trivial length, $o(CD)$. On the positive side, we construct $O(C+D+\log^2 n)$-length schedules in any $n$-node network. These schedules are near-optimal, since our lower bound shows that this length cannot be improved to $O(C+D) + o(\log n)$.

翻译：我们研究同时多播的存储和前方包路由问题, 即多个包必须尽快在给定树上传送多个包件。 这是Leighton、 Maggs 和 Rao 的原始工程的自然概括, 它解决了对单播的这个问题, 即所有树都是路径的情况。 它们显示存在非同步最佳的 O( C + D) $- 长的排程, 即拥堵 $C + D) 是一个边缘发送的包的最大数量, 而 3D 美元是树的最大深度。 这比小的 $O( CD) 长的排程要好得多。 我们证明多播的集成任务范围要小, 这表明并不总是有非三角长度的排程, $o( CD) 。 在正反面, 我们在任何 $( C+ D) log2 n 网络中建造 $O( + log) $- 长的排程表。 这些排程是近于最理想的, 因为我们的 n- bure 显示这一长度不能改进到 $\ ( C+ o) oD) 。