同时多播的近优调度
Near-Optimal Schedules for Simultaneous Multicasts
摘要：
我们研究的存储和转发的数据包路由问题，同时组播，其中多个数据包被转发沿给定的树尽可能快。这是Leighton，Maggs和Rao的开创性工作的自然推广，解决了单播的这个问题，即所有树都是路径的情况。他们证明了存在渐近最优的$O(C + D)$长度调度，其中拥塞$C$是在边缘上发送的数据包的最大数量，膨胀$D$是树的最大深度。这改进了普通的$O(CD)$长度调度。我们证明了一个下界的组播，这表明并不总是存在非平凡的长度，$o(CD)$的时间表。在积极的一面，我们构造$O(C+D+\log^2 n)$长度的调度在任何$n$节点网络。这些时间表接近最优，因为我们的下限表明该长度不能改进为$O(C+D) + o(\log n)$。
英文摘要：
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 $O(C+D) + o(\log n)$.
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