O（congestion + dilation）包路由的一个简单证明
A simpler proof for O(congestion + dilation) packet routing
摘要：
在存储转发路由问题中，数据包必须沿着给定的路径路由，使得最新数据包的到达时间最小化。Leighton，Maggs和Rao的一个突破性的结果表明，这总是可以在时间O（拥塞+膨胀）内完成，其中拥塞是使用边的最大路径数，膨胀是路径的最大长度。然而，分析是相当《双城之战》和复杂的，并通过迭代改进不可行的调度来工作。在这里，我们提供了一个更容易理解的分析，它是基于条件期望。像[LMR 94]一样，我们更简单的分析也保证了恒定大小的边缘缓冲区就足够了。此外，这是一个开放的问题，例如由Wiese陈述，是否存在任何情况下，所有调度都需要至少（1 + k）*（拥塞+扩张）步骤，对于常数k> 0。我们肯定地回答这个问题，利用概率结构。
英文摘要：
In the store-and-forward routing problem, packets have to be routed along given paths such that the arrival time of the latest packet is minimized. A groundbreaking result of Leighton, Maggs and Rao says that this can always be done in time O(congestion + dilation), where the congestion is the maximum number of paths using an edge and the dilation is the maximum length of a path. However, the analysis is quite arcane and complicated and works by iteratively improving an infeasible schedule. Here, we provide a more accessible analysis which is based on conditional expectations. Like [LMR94], our easier analysis also guarantees that constant size edge buffers suffice. Moreover, it was an open problem stated e.g. by Wiese, whether there is any instance where all schedules need at least (1 + epsilon)*(congestion + dilation) steps, for a constant epsilon > 0. We answer this question affirmatively by making use of a probabilistic construction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
