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Reconfiguring Arrays with Faults Part I: WorstCase Faults
 SIAM Journal on Computing
, 1997
"... . In this paper we study the ability of arraybased networks to tolerate worstcase faults. We show that an N \Theta N twodimensional array can sustain N 1\Gammaffl worstcase faults, for any fixed ffl ? 0, and still emulate T steps of a fully functioning N \Theta N array in O(T +N) steps, i.e., ..."
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. In this paper we study the ability of arraybased networks to tolerate worstcase faults. We show that an N \Theta N twodimensional array can sustain N 1\Gammaffl worstcase faults, for any fixed ffl ? 0, and still emulate T steps of a fully functioning N \Theta N array in O(T +N) steps, i.e., with only constant slowdown. Previously it was known only that an array could tolerate a constant number of faults with constant slowdown. We also show that if faulty nodes are allowed to communicate, but not compute, then an Nnode onedimensional array can tolerate log k N worstcase faults, for any constant k ? 0, and still emulate a faultfree array with constant slowdown, and this bound is tight. Key words. fault tolerance, arraybased network, mesh network, network emulation AMS subject classifications. 68M07, 68M10, 68M15, 68Q68 1. Introduction. In a truly large parallel computer, some components are bound to fail. Knowing this, a programmer can write software that explicitly cope...
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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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...
A Critical Look at Three of Parallel Computing's Maxims
 In International Symposium on Parallel Architectures, Algorithms and Networks
, 1995
"... This paper takes a critical look at the following three maxims. 1. Parallel architecture is converging on a design based on commodity microprocessor chips. 2. Wormhole routing is decidedly more efficient than storeandforward routing. 3. The PRAM is an unrealistically ideal model of computation. 1 ..."
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This paper takes a critical look at the following three maxims. 1. Parallel architecture is converging on a design based on commodity microprocessor chips. 2. Wormhole routing is decidedly more efficient than storeandforward routing. 3. The PRAM is an unrealistically ideal model of computation. 1 Introduction The last few years have seen the introduction of a large number of parallel computers, as well as the failures of several manufacturers. As the machines have been released, they have been thoroughly evaluated, and a wide range of benchmark data is now available. Furthermore, in this time our expertise in programming and extracting performance from parallel machines has greatly increased, a theory of parallel and network algorithms has developed, and our understanding of the modeling process has improved. Hence, now seems a propitious time to take a critical look at our maxims. 2 Architectural convergence Parallel architecture is converging on a design based on commodity micr...
Managing Scheduled Routing With A HighLevel Communications Language
, 1997
"... ... among processors. This thesis addresses the programming of systems (such as the NuMesh) that handle routing via highspeed reprogrammable scheduled routers on each node. A portable `communications language', COP, used to express communications requirements, is presented. Using scheduled rou ..."
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... among processors. This thesis addresses the programming of systems (such as the NuMesh) that handle routing via highspeed reprogrammable scheduled routers on each node. A portable `communications language', COP, used to express communications requirements, is presented. Using scheduled routers to control data motion through the network has two advantages. First, by performing offline path scheduling for messages based on information extracted from the application, latency and congestion can be improved. Second, by removing the need for online decision making, such routers can run at extremely high speeds, further decreasing latencies and increasing performance. Simple
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"... Abstract This paper analyzes the effect of virtual channels on the performance of wormhole routing algorithms. We show that in a network in which each edge can emulate up to q virtual channels, it is possible to route any set of bbit messages whose paths have congestion c and dilation d in (b + d)c ..."
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Abstract This paper analyzes the effect of virtual channels on the performance of wormhole routing algorithms. We show that in a network in which each edge can emulate up to q virtual channels, it is possible to route any set of bbit messages whose paths have congestion c and dilation d in (b + d)c(d log d) 1=q 2 O(log \Lambda (c=d)) bitsteps. We also prove a nearly matching lower bound, i.e., for any values of c, d, q, and b, where c ss d and b * d, we show how to construct a network and a set of bbit messages whose paths have congestion c and dilation d that require \Omega (bcd
VIRTUAL CHANNELS IN WORMHOLE ROUTERS
, 1999
"... This paper analyzes the impact of virtual channels on the performance of wormhole routing algorithms. We study wormhole routing on network in which each physical channel, i.e., communication link, can support up to B virtual channels. We show that it is possible to route any set of messages with L f ..."
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This paper analyzes the impact of virtual channels on the performance of wormhole routing algorithms. We study wormhole routing on network in which each physical channel, i.e., communication link, can support up to B virtual channels. We show that it is possible to route any set of messages with L flits each, whose paths have congestion C and dilation D in O((L+ D) C(D log D) 1 B B) flit steps, where a flit step is the time taken to transmit B flits, i.e., one flit per virtual channel, across a physical channel. 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+0(1)) D, we show how to construct a network and a set of Lflit messages whose paths have congestion C and dilation D that require 0(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 significantly larger than B. We also present a simple randomized wormhole routing algorithm for the butterfly network. The algorithm routes any qrelation on the inputs and outputs