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 [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. © 2013 Springer-Verlag.
CITATION STYLE
Rothvoß, T. (2013). A simpler proof for O(congestion + dilation) packet routing. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7801 LNCS, pp. 336–348). https://doi.org/10.1007/978-3-642-36694-9_29
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