On the hardness of approximating optimum schedule problems in store and forward networks
IEEE/ACM Transactions on Networking (TON)
Distributed packet switching in arbitrary networks
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Universal O(congestion + dilation + log1+&egr;N) local control packet switching algorithms
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Shortest-path routing in arbitrary networks
Journal of Algorithms
Universal Routing Strategies for Interconnection Networks
Universal Routing Strategies for Interconnection Networks
A Constant-Factor Approximation Algorithm for Packet Routing and Balancing Local vs. Global Criteria
SIAM Journal on Computing
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Concentration of Measure for the Analysis of Randomized Algorithms
Concentration of Measure for the Analysis of Randomized Algorithms
Real-Time Message Routing and Scheduling
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
A constructive proof of the general lovász local lemma
Journal of the ACM (JACM)
Universal packet routing with arbitrary bandwidths and transit times
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Hardness of Approximating Flow and Job Shop Scheduling Problems
Journal of the ACM (JACM)
Packet routing: complexity and algorithms
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Constraint satisfaction, packet routing, and the lovasz local lemma
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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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 $O(\textrm{congestion} + \textrm{dilation})$, 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 $(1+\varepsilon)\cdot(\textrm{congestion}+\textrm{dilation})$ steps, for a constant ε0. We answer this question affirmatively by making use of a probabilistic construction.