Efficient Schemes for Parallel Communication
Journal of the ACM (JACM)
Average case analysis of greedy routing algorithms on arrays
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
The efficiency of greedy routing in hypercubes and butterflies
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Simple algorithms for routing on butterfly networks with bounded queues
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Bounds on the greedy routing algorithm for array networks
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
Bounding delays in packet-routing networks
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Universal continuous routing strategies
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
Dynamic deflection routing on arrays (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Greedy dynamic routing on arrays
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Queueing analysis of oblivious packet-routing networks
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Tight bounds for the performance of longest in system on DAGs
Journal of Algorithms
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We prove a sufficient condition for the stability of dynamic packet routing algorithms. Our approach reduces the problem of steady state analysis to the easier and better understood question of static routing. We show that certain high probability and worst case bounds on the quasi-static (finite past) performance of a routing algorithm imply bounds on the performance of the dynamic version of that algorithm. Our technique is particularly useful in analyzing routing on networks with bounded buffers where complicated dependices make standard queuing techniques inapplicable.We present several applications of our approach. In all cases we start from a known static algorithm, and modify it to fit our framework. In particular we give the first dynamic algorithms for routing on a butterfly or two-dimensional mesh with bounded buffers. Both the injection rate for which the algorithm is stable, and the expected time a packet spends in the system are optimal up to constant factors. Our approach is also applicable to the recently introduced adversarial input model.