Efficient Schemes for Parallel Communication
Journal of the ACM (JACM)
Routing, merging, and sorting on parallel models of computation
Journal of Computer and System Sciences
The efficiency of greedy routing in hypercubes and butterflies
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
General purpose parallel architectures
Handbook of theoretical computer science (vol. A)
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Randomized parallel communication (Preliminary Version)
PODC '82 Proceedings of the first ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Communication issues in parallel computation
Communication issues in parallel computation
Methods for message routing in parallel machines
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
On randomization in sequential and distributed algorithms
ACM Computing Surveys (CSUR)
Minimal adaptive routing on the mesh with bounded queue size
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
On the benefit of supporting virtual channels in wormhole routers
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
On the communication throughput of buffered multistage interconnection networks
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
The performance of simple routing algorithms that drop packets
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
Randomized protocols for low-congestion circuit routing in multistage interconnection networks
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Scheduling time-constrained communication in linear networks
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
On Evil Twin Networks and the Value of Limited Randomized Routing
IEEE Transactions on Parallel and Distributed Systems
A general approach to dynamic packet routing with bounded buffers
Journal of the ACM (JACM)
A Parallel Algorithm for Reconfiguring a Multibutterfly Network with Faulty Switches
IEEE Transactions on Computers
A collision model for randomized routing in fat-tree networks
Journal of Parallel and Distributed Computing
Towards programming on the moving threads architecture
Proceedings of the 11th International Conference on Computer Systems and Technologies and Workshop for PhD Students in Computing on International Conference on Computer Systems and Technologies
Stochastic comparisons for rooted butterfly networks and tree networks, with random environments
Information Sciences: an International Journal
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This paper examines several simple algorithms for routing packets on butterfly networks with bounded queues. We show that for any pure queuing protocol, a routing problem in which each of the N inputs sends a packet to a randomly chosen output requires O(log N) steps, with high probability, provided that the queue size is a sufficiently large, but fixed, constant. We also show that for any deterministic non-predictive queuing protocol, there exists a permutation that requires &OHgr;(N/q log N) time to route, where q is the maximum queue size. We present a new algorithm for routing a random problem on a fully-loaded butterfly with bounded-size queues in O(log N) steps, with high probability. The algorithm is simpler than the previous algorithms of Ranade and Pippenger because it does not use ghost messages, it does not compare the ranks or destinations of packets as they pass through a switch, and it cannot deadlock. Finally, using Valiant's idea of random intermediate destinations, we generalize a result of Koch's by showing that, if each wire can support q messages, then for any permutation, the expected number of messages that succeed in locking down paths from their origins to their destinations in back-to-back butterflies is &OHgr;(N(log N1/q). The analysis also applies to store-and-forward algorithms that drop packets if they attempt to enter full queues.