A simpler proof for O(congestion + dilation) packet routing

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 amore 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 [Wie11], whether there is any instance where all schedules need at least (1+ ε) · (congestion+dilation) steps, for a constant ε > 0. We answer this question affirmatively by making use of a probabilistic construction.