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Universal Algorithms for StoreandForward and Wormhole Routing
 IN PROC. OF THE 28TH ACM SYMP. ON THEORY OF COMPUTING (STOC
, 1996
"... In this paper we present routing algorithms that are universal in the sense that they route messages along arbitrary (simple) paths in arbitrary networks. The algorithms are analyzed in terms of the number of messages being routed, the maximum number of messages that must cross any edge in the netwo ..."
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Cited by 34 (18 self)
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In this paper we present routing algorithms that are universal in the sense that they route messages along arbitrary (simple) paths in arbitrary networks. The algorithms are analyzed in terms of the number of messages being routed, the maximum number of messages that must cross any edge in the network (edge congestion), the maximum number of edges that a message must cross (dilation), the buffer size, and the bandwidth of the links. We present two main results, both of which have applications to universal storeand forward routing and universal wormhole routing. Our results yield significant performance improvements over all previously known universal routing algorithms for a wide range of parameters, and they even improve many time bounds for standard networks. In addition, we present adaptations of our main results for routing along shortest paths in arbitrary networks, and for routing in leveled networks, nodesymmetric networks, edgesymmetric networks, expanders, butterflies, and ...
Packet Routing In FixedConnection Networks: A Survey
, 1998
"... We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing ..."
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Cited by 29 (3 self)
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We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing, fault tolerant routing, and related sorting results. We also provide a list of unsolved problems and numerous references.
A General Theory for Deadlock Avoidance in WormholeRouted Networks
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 1998
"... Most machines of the last generation of distributed memory parallel computers possess specific routers which are used to exchange messages between nonneighboring nodes in the network. Among the several technologies, wormhole routing is usually prefered because it allows low channelsetup time, and ..."
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Cited by 23 (2 self)
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Most machines of the last generation of distributed memory parallel computers possess specific routers which are used to exchange messages between nonneighboring nodes in the network. Among the several technologies, wormhole routing is usually prefered because it allows low channelsetup time, and reduces the dependency between latency and internode distance. However, wormhole routing is very susceptible to deadlock because messages are allowed to hold many resources while requesting others. Therefore, designing deadlockfree routing algorithms using few hardware facilities is a major problem for wormholerouted networks. In this paper, we describe a general theoretical framework for the study of deadlockfree routing functions. We give a general definition of what can be a routing function. This definition captures many specific definitions of the literature (e.g., vertexdependent, inputdependent, sourcedependent, pathdependent, etc.). Using our definition, we give a necessary an...
Universal Wormhole Routing
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 1993
"... In this paper, we examine the wormhole routing problem in terms of the "congestion" c and "dilation" d for a set of packet paths. We show, with mild restrictions, that there is a simple randomized algorithm for routing any set of P packets in O (cdj + cLj log P ) time with high probability, where L ..."
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Cited by 20 (3 self)
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In this paper, we examine the wormhole routing problem in terms of the "congestion" c and "dilation" d for a set of packet paths. We show, with mild restrictions, that there is a simple randomized algorithm for routing any set of P packets in O (cdj + cLj log P ) time with high probability, where L is the number of flits in a packet, and j = minfd; Lg; only a constant number of flits are stored in each queue at any time. Using this result, we show that a fattree network of area \Theta(A) can simulate wormhole routing on any network of comparable area with O(log 3 A) slowdown, when all worms have the same length. Variablelength worms are also considered. We run some simulations on the fattree which show that not only does wormhole routing tend to perform better than the more heavily studied storeandforward routing in this context, but that performance superior to our provable bound is attainable in practice.
Modeling parallel bandwidth: Local vs. global restrictions
"... Recently there has been an increasing interest in models of parallel computation that account for the bandwidth limitations in communication networks. Some models (e.g., bsp and logp) account for bandwidth limitations using a perprocessor parameter g> 1, such that eachpro cessor can send/receive at ..."
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Cited by 15 (4 self)
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Recently there has been an increasing interest in models of parallel computation that account for the bandwidth limitations in communication networks. Some models (e.g., bsp and logp) account for bandwidth limitations using a perprocessor parameter g> 1, such that eachpro cessor can send/receive at most h messages in g h time. Other models (e.g., pram(m)) account for bandwidth limitations as an aggregate parameter m<p, such thatthe p processors can send at most m messages in total at each step. This paper provides the rst detailed study of the algorithmic implications of modeling parallel bandwidth as a perprocessor (local) limitation versus an aggregate (global) limitation. We consider a number of basic problems
Supporting Sets of Arbitrary Connections on iWarp Through Communication Context Switches
 In Proc. SPAA
, 1993
"... In this paper we introduce the ConSet communication model for distributed memory parallel computers. The communication needs of an application program can be satisfied by some arbitrary set of connections which are partitioned into discrete phases. A communication context switch is used to select th ..."
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Cited by 15 (6 self)
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In this paper we introduce the ConSet communication model for distributed memory parallel computers. The communication needs of an application program can be satisfied by some arbitrary set of connections which are partitioned into discrete phases. A communication context switch is used to select the active phase. We present an implementation of the ConSet model on the iWarp and describe its performance characteristics, contrasting it to a message passing implementation on the same machine. Our implementation demonstrates how one existing parallel computer can function as a “reconfigurable network ” without needing a new processor interconnect technology. The ConSet model works best when communication patterns can be optimized at compile time. We examine the interactions of the target architecture with the algorithmic problems encountered designing a communication compiler to effectively partition, route, and schedule connections. We built a prototype communication compiler for our iWarp implementation, and are using it to generate iWarp code. Looking at basic communication patterns as well as patterns generated by an iterative finite element PDE solver, we compare ConSet’s performance (using the compiler’s schedules) to that of message passing. Our experiments suggestthat ConSet communication offers a performance advantage over messagepassing in applications where the communication pattern is known at compile time. 1
How Much Can Hardware Help Routing?
"... . We study the extent to which complex hardware can speed up routing. Specifically, we consider the following questions. How much does adaptive routing improve over oblivious routing? How much does randomness help? How does it help if each node can have a large number of neighbors? What benefit is a ..."
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Cited by 15 (3 self)
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. We study the extent to which complex hardware can speed up routing. Specifically, we consider the following questions. How much does adaptive routing improve over oblivious routing? How much does randomness help? How does it help if each node can have a large number of neighbors? What benefit is available if a node can send packets to several neighbors within a single time step? Some of these features require complex networking hardware, and it is thus important to investigate whether the performance justifies the investment. By varying these hardware parameters, we obtain a hierarchy of time bounds for worstcase permutation routing.
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 14 (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.
Nearly tight bounds for wormhole routing
 In Proceedings of the 35th Annual Symposium on Foundations of Computer Science
, 1994
"... We present nearly tight bounds for wormhole routing on Butterfly networks which indicate it is fundamentally different from storeandforward packet routing. For instance, consider the problem of routing N log N (randomly generated) log N length messages from the inputs to the outputs of an N i ..."
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Cited by 13 (0 self)
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We present nearly tight bounds for wormhole routing on Butterfly networks which indicate it is fundamentally different from storeandforward packet routing. For instance, consider the problem of routing N log N (randomly generated) log N length messages from the inputs to the outputs of an N input Butterfly. We show that with high probability that this must take time at least fl(10g3 N/(loglog N)’). The best lower bound known earlier was Q(log2 N), which is simply the frit congestion in each link. Thus our lower bound shows that wormhole routing (unlike storeandforwardrouting) is very ineffective in utilizing communication links. We also give a routing algorithm which nearly matches our lower bound. That is, we show that with high probability the time is O(10g3 N log log N), which improves upon the previous best bound of O(10g4 N). Our method also extends to other networks such as the twodimensional mesh, where it is nearly optimal. Finally, we consider the problem of ofline wormhole routing, where we give optimal algorithms for trees and multidimensional meshes.