Routing, merging, and sorting on parallel models of computation
Journal of Computer and System Sciences
Routing and sorting on mesh-connected arrays (extended abstract)
VLSI Algorithms and Architectures
A 2n-2 step algorithm for routing in an nxn array with constant size queues
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Average case analysis of greedy routing algorithms on arrays
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Tight bounds for oblivious routing in the hypercube
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
System design of the J-Machine
AUSCRYPT '90 Proceedings of the sixth MIT conference on Advanced research in VLSI
Oblivious routing with limited buffer capacity
Journal of Computer and System Sciences
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
Constant queue routing on a mesh
Journal of Parallel and Distributed Computing
The DASH prototype: implementation and performance
ISCA '92 Proceedings of the 19th annual international symposium on Computer architecture
Planar-adaptive routing: low-cost adaptive networks for multiprocessors
ISCA '92 Proceedings of the 19th annual international symposium on Computer architecture
The design of the Caltech Mosaic C multicomputer
Proceedings of the 1993 symposium on Research on integrated systems
Fast deflection routing for packets and worms
PODC '93 Proceedings of the twelfth annual ACM symposium on Principles of distributed computing
How much can hardware help routing?
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Hot-potato routing on processor arrays
SPAA '93 Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures
Bounds on evacuation time for deflection routing
Distributed Computing
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An adaptive routing algorithm is one in which the path a packet takes from its source to its destination may depend on other packets it encounters. Such algorithms potentially avoid network bottlenecks by routing packets around “hot spots.” Minimal adaptive routing algorithms have the additional advantage that the path each packet takes is a shortest one.For a large class of minimal adptive routing algorithms, we present an &OHgr;(n2/k2) bound on the worst case time to route a static permutation of packets on an n × n mesh or torus with nodes that can hold up to k ≥ 1 packets each. This is the first nontrivial lower bound on adaptive routing algorithms. The argument extends to more general routing problems, such as the h-h routing problem. It also extends to a large class of dimension order routing algorithms, yielding an &OHgr;(n2/k) time bound.To complement these lower bounds, we present two upper bounds. One is an O(n2/k) time dimension order routing algorithm that matches the lower bound. The other is the first instance of a minimal adaptive routing algorithm that achieves O(n) time with constant sized queues per node. We point out why the latter algorithm is outside the model of our lower bounds.