A simpler proof for O(congestion + dilation) packet routing
Abstract
In the storeandforward 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2012
 arXiv:
 arXiv:1206.3718
 Bibcode:
 2012arXiv1206.3718R
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Discrete Mathematics;
 Mathematics  Combinatorics;
 F.2.0