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21
Randomized routing and sorting on fixedconnection networks
 JOURNAL OF ALGORITHMS
, 1994
"... This paper presents a general paradigm for the design of packet routing algorithms for fixedconnection networks. Its basis is a randomized online algorithm for scheduling any set of N packets whose paths have congestion c on any boundeddegree leveled network with depth L in O(c + L + log N) steps ..."
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Cited by 86 (13 self)
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This paper presents a general paradigm for the design of packet routing algorithms for fixedconnection networks. Its basis is a randomized online algorithm for scheduling any set of N packets whose paths have congestion c on any boundeddegree leveled network with depth L in O(c + L + log N) steps, using constantsize queues. In this paradigm, the design of a routing algorithm is broken into three parts: (1) showing that the underlying network can emulate a leveled network, (2) designing a path selection strategy for the leveled network, and (3) applying the scheduling algorithm. This strategy yields randomized algorithms for routing and sorting in time proportional to the diameter for meshes, butterflies, shuffleexchange graphs, multidimensional arrays, and hypercubes. It also leads to the construction of an areauniversal network: an Nnode network with area Θ(N) that can simulate any other network of area O(N) with slowdown O(log N).
Fast Algorithms for Routing Around Faults in Multibutterflies and RandomlyWired Splitter Networks
 In IEEE Transactions on Computers
, 1992
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Universal Continuous Routing Strategies
 IN PROC. OF THE 8TH ACM SYMP. ON PARALLEL ALGORITHMS AND ARCHITECTURES (SPAA
, 1996
"... In this paper we present routing protocols that are universal in the sense that they route messages along arbitrary (simple or shortest) paths in arbitrary networks. We study these protocols under a stochastic model of continuous message generation. The performance of such protocols is characterized ..."
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Cited by 24 (5 self)
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In this paper we present routing protocols that are universal in the sense that they route messages along arbitrary (simple or shortest) paths in arbitrary networks. We study these protocols under a stochastic model of continuous message generation. The performance of such protocols is characterized by three parameters: the maximum message generation rate for which the protocol is stable, the expected delay of a message from generation to service, and the time the protocol needs to recover from worst case scenarios. Our main results are a universal continuous storeandforward routing protocol and a universal continuous wormhole routing protocol. Both protocols yield significant performance improvements over all previously known continuous routing protocols. In addition, we present adaptations of our main results to continuous routing in nodesymmetric networks, butterflies, and meshes.
Randomized Protocols for LowCongestion Circuit Routing in Multistage Interconnection Networks
"... In this paper we study randomized algorithms for circuit switching on multistage networks related to the butterfly. We devise algorithms that route messages by constructing circuits (or paths) for the messages with small congestion, dilation, and setup time. Our algorithms are based on the idea of h ..."
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Cited by 16 (5 self)
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In this paper we study randomized algorithms for circuit switching on multistage networks related to the butterfly. We devise algorithms that route messages by constructing circuits (or paths) for the messages with small congestion, dilation, and setup time. Our algorithms are based on the idea of having each message choose a route from two possibilities, a technique that has previously proven successful in simpler load balancing settings. As an application of our techniques, we propose a novel design for a data server.
Simple Algorithms for Routing on Butterfly Networks with Bounded Queues (Extended Abstract)
 IN PROCEEDINGS OF THE 24TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1992
"... The analysis also applies to storeandforward algorithms that drop packets if they attempt to enter full queues. We show ..."
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Cited by 14 (8 self)
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The analysis also applies to storeandforward algorithms that drop packets if they attempt to enter full queues. We show
Empirical Evaluation of RandomlyWired Multistage Networks (Extended Abstract)
, 1990
"... In this paper, we present experimental data indicating that multistage interconnection networks with randomly positioned wires are likely to be substantially better for message routing applications than traditional multistage networks such as the butterfly. Data is presented for a variety of routin ..."
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Cited by 13 (2 self)
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In this paper, we present experimental data indicating that multistage interconnection networks with randomly positioned wires are likely to be substantially better for message routing applications than traditional multistage networks such as the butterfly. Data is presented for a variety of routing models, including storeandforward routing, cutthrough routing, and circuit switching, as well as for scenarios in which a potentially large number of switches are faulty. In most every situation, we find that randomlywired networks outperform traditional networks with the same amount of hardware. In some cases, the differences are dramatic, particularly when several switches in the network are faulty. Overall, the data provides excellent empirical confirmation of recent theoretical work.
On the Benefit of Supporting Virtual Channels in Wormhole Routers
 In Proceedings of the 8th Annual ACM Symposium on Parallel Algorithms and Architectures
, 1996
"... This paper analyzes the impact of virtual channels on the performance of wormhole routing algorithms. We show that in any network in which each physical channel, i.e., communication link, can support up to B virtual channels, it is possible to route any set of messages with L flits each, whose paths ..."
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Cited by 10 (4 self)
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This paper analyzes the impact of virtual channels on the performance of wormhole routing algorithms. We show that in any network in which each physical channel, i.e., communication link, can support up to B virtual channels, it is possible to route any set of messages with L flits each, whose paths have congestion C and dilation D in (L + D)C(D log D) 1=B 2 O(log (C=D)) =B flit steps, where a flit step is the time taken to transmit a single flit across a link. We also prove a nearly matching lower bound, i.e., for any values of C, D, B, and L, where C; D B + 1 and L = (1 +\Omega\Gamma302 D, we show how to construct a network and a set of Lflit messages whose paths have congestion C and dilation D that require\Omega\Gamma LCD 1=B =B) flit steps to route. These upper and lower bounds imply that increasing the buffering capacity and the bandwidth of each physical channel by a factor of B can speed up a wormhole routing algorithm by a superlinear factor, i.e., a factor signi...
On the Communication Throughput of Buffered Multistage Interconnection Networks
 PROC. OF THE 8TH ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 1996
"... Multistage networks (MIN) are used as interconnection structure in a large number of applications. Their performance is mainly determined by their communication throughput which, in most cases, has to be investigated by timeconsuming simulations or approximated by simple models. In this paper, we i ..."
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Cited by 7 (0 self)
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Multistage networks (MIN) are used as interconnection structure in a large number of applications. Their performance is mainly determined by their communication throughput which, in most cases, has to be investigated by timeconsuming simulations or approximated by simple models. In this paper, we investigate the steady state throughput of single buffered multistage interconnection networks using the so called relaxed blocking model, where a message is deleted, if the receiving buffer is occupied. We derive upper and lower bounds on the throughput of MINs of arbitrary height and show that the throughput of singlebuffered networks is an order of magnitude higher than the throughput of nonbuffered MINs. In detail we show, that the throughput is \Theta(n= p log n) if n is the size of the network. Because the timedynamic of finite buffered MINs defies each marcov or semimarcov approach, we analyze the the equilibriumsituation of the network and give tight upper and lower bounds on t...
A parallel algorithm for reconfiguring a multibutterfly network with faulty switches
 IEEE Transactions on Computers
, 1994
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An Analysis of Oblivious and Adaptive Routing in Optical Networks With Wavelength Translation
 IEEE/ACM Transactions on networking
, 2001
"... We present an analysis for both oblivious and adaptive routing in regular, alloptical networks with wavelength translation. Our approach is simple, computationally inexpensive, accurate for both low and high network loads, and the first to analyze adaptive routing with wavelength translation in wav ..."
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We present an analysis for both oblivious and adaptive routing in regular, alloptical networks with wavelength translation. Our approach is simple, computationally inexpensive, accurate for both low and high network loads, and the first to analyze adaptive routing with wavelength translation in wavelength division multiplexed (WDM) networks while also providing a simpler formulation of oblivious routing with wavelength translation. Unlike some previous analyses which use the link independence blocking assumption and the call dropping (loss) model (where blocked calls are cleared), we account for the dependence between the acquisition of wavelengths on successive links of a session's path and use a lossless model (where blocked calls are retried at a later time). We show that the throughput per wavelength increases superlinearly (as expected) as we increase the number of wavelengths per link, due both to additional capacity and more efficient use of this capacity; however, the extent of this superlinear increase in throughput saturates rather quickly to a linear increase. We also examine the effect that adaptive routing can have on performance. The analytical methodology that we develop can be applied to any vertex and edge symmetric topology, and with modifications, to any vertex symmetric (but not necessarily edge symmetric) topology. We find that, for the topologies we examine, providing at most one alternate link at every hop gives a perwavelength throughput that is close to that achieved by oblivious routing with twice the number of wavelengths per link. This suggests some interesting possibilities for network provisioning in an alloptical network. We verify the accuracy of our analysis for both oblivious and adaptive routing via simulations for the torus and hyp...