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21
The Turn Model for Adaptive Routing
 In Proceedings of the International Symposium on Computer Architecture
, 1992
"... We present a model for designing wormhole routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive. A unique feature of this model is that it is not based on adding physical or virtual channels to network topologies (though it can be applied to networks ..."
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Cited by 281 (6 self)
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We present a model for designing wormhole routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive. A unique feature of this model is that it is not based on adding physical or virtual channels to network topologies (though it can be applied to networks with extra channels). Instead, the model is based on analyzing the directions in which packets can turn in a network and the cycles that the turns can form. Prohibiting just enough turns to break all of the cycles produces routing algorithms that are deadlock free, livelock free, minimal or nonminimal, and maximally adaptive for the network. In this paper, we focus on the two most common network topologies for wormhole routing, ndimensional meshes and kary ncubes, without extra channels. In an ndimensional mesh, just a quarter of the turns must be prohibited to prevent deadlock. The remaining three quarters of the turns permit partial adaptiveness in routing. Partially adaptive routing ...
An EulerPathBased Multicasting Model for WormholeRouted Networks with MultiDestination Capability
, 1996
"... This research is supported by the National Science Council of the Republic of China under Grant # NSC862213E008029 and Grant # NSC862213E216021. 1 Recently, wormhole routers with multidestination capability have been proposed to support fast multicast in a multicomputer network. In thi ..."
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Cited by 29 (5 self)
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This research is supported by the National Science Council of the Republic of China under Grant # NSC862213E008029 and Grant # NSC862213E216021. 1 Recently, wormhole routers with multidestination capability have been proposed to support fast multicast in a multicomputer network. In this paper, we develop a new multicasting model for such networks based on the concept of Euler path/circuit in graph theory. The model can support multiple concurrent multicasts freely from deadlock and can be applied to any network which is Eulerian or is Eulerian after some links being removed. No virtual channels are needed. In particular, we demonstrate the potential of this model by showing its faulttolerant capability in supporting multicasting in the currently popular torus/mesh topology of any dimension with regular fault patterns (such as single node, block, Lshape, +shape, Ushape, and Hshape) and even irregular fault patterns. It is the first multicasting model known t...
FaultTolerant Wormhole Routing in Meshes
 IN TWENTYTHIRD ANNUAL INT. SYMP. ON FAULTTOLERANT COMPUTING
, 1993
"... Previous methods of making wormholerouted meshes fault tolerant have been based on adding virtual channels to these networks. This paper proposes an alternative method, one based on the turn model for designing wormhole routing algorithms. Whether a direct network contains virtual channels or not, ..."
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Cited by 25 (0 self)
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Previous methods of making wormholerouted meshes fault tolerant have been based on adding virtual channels to these networks. This paper proposes an alternative method, one based on the turn model for designing wormhole routing algorithms. Whether a direct network contains virtual channels or not, the turn model produces routing algorithms that are deadlock free, very adaptive, minimal or nonminimal, and livelock free. This paper illustrates how to modify the routing algorithms produced by the turn model to encompass dynamic faults. The paper first describes how to modify the negativefirst routing algorithm, which the turn model produces for ndimensional meshes without virtual channels, to make it onefault tolerant. Simulations of the onefault tolerant routing algorithm and other minimal and nonminimal routing algorithms in a twodimensional mesh indicate that misrouting increases communication latencies significantly at high throughputs. The conclusion is that misrouting should ...
Wormhole Routing Techniques for Directly Connected Multicomputer Systems
 ACM Computing Surveys
, 1998
"... Wormhole routing has emerged as the most widely used switching technique in massively parallel computers. We present here a detailed survey of various techniques for enhancing the performance and reliability of the wormhole routing schemes in directly connected networks. We start with an overview of ..."
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Cited by 24 (0 self)
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Wormhole routing has emerged as the most widely used switching technique in massively parallel computers. We present here a detailed survey of various techniques for enhancing the performance and reliability of the wormhole routing schemes in directly connected networks. We start with an overview of the direct network topologies and a comparison of various switching techniques. Next, the characteristics of wormhole routing mechanism are described in detail along with the theory behind deadlockfree routing. The performance of routing algorithms depends on the selection of path between the source and the destination, the network traffic, and the router design. The routing algorithms are implemented in the router chips. We outline the router characteristics and describe the functionality of various elements of the router. Depending on the usage of paths between the source and the destination, the routing algorithms are classified as deterministic, fully adaptive, and partially adaptive. ...
Adaptive FaultTolerant DeadlockFree Routing in Meshes and Hypercubes
 IEEE Transactions on Computers
, 1995
"... We present an adaptive deadlockfree routing algorithm which decomposes a given network into two virtual interconnection networks, V IN 1 and V IN 2 . V IN 1 supports deterministic deadlockfree routing, and V IN 2 supports fullyadaptive routing. Whenever a channel in V IN 1 or V IN 2 is available, ..."
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Cited by 22 (0 self)
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We present an adaptive deadlockfree routing algorithm which decomposes a given network into two virtual interconnection networks, V IN 1 and V IN 2 . V IN 1 supports deterministic deadlockfree routing, and V IN 2 supports fullyadaptive routing. Whenever a channel in V IN 1 or V IN 2 is available, it can be used to route a message. Each node is identified to be in one of three states: safe, unsafe, and faulty. The unsafe state is used for deadlockfree routing, and an unsafe node can still send and receive messages. When nodes become faulty/unsafe, some channels in V IN 2 around the faulty/unsafe nodes are used as the detours of those channels in V IN 1 passing through the faulty/unsafe nodes, i.e., the adaptability in V IN 2 is transformed to support faulttolerant deadlockfree routing. Using information on the state of each node's neighbors, we have developed an adaptive faulttolerant deadlockfree routing scheme for ndimensional meshes and hypercubes with only two virtual channe...
Reducing Cache Invalidation Overheads in Wormhole Routed DSMs Using Multidestination Message Passing
 In International Conference on Parallel Processing
, 1996
"... : Directorybased distributed shared memory (DSM) systems have drawn high interests in parallel computing research and industry in recent years. Current generation systems are limited to using pointtopoint messages for cache invalidation requests and associated acknowledgments. Such an approach in ..."
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Cited by 20 (10 self)
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: Directorybased distributed shared memory (DSM) systems have drawn high interests in parallel computing research and industry in recent years. Current generation systems are limited to using pointtopoint messages for cache invalidation requests and associated acknowledgments. Such an approach incurs a large number of control messages, heavy network traffic, and high occupancy at home nodes. In this paper we present a new approach to reduce cache invalidation overheads. We introduce a set of multidestinationbased reservation and gather worms to distribute invalidation requests and collect acknowledgments. Six different grouping schemes are investigated in generating such multidestination worms in order to implement fullymapped directorybased cache coherence on networks using deterministic (ecube) or adaptive (turnmodel) wormhole routing. These schemes are evaluated for different applications and 2D mesh configurations through executiondriven simulation. The interplay among ov...
A Necessary and Sufficient Condition for DeadlockFree Wormhole Routing
 Journal of Parallel and Distributed Computing
, 1996
"... An important open problem in wormhole routing has been to find a necessary and sufficient condition for deadlockfree adaptive routing. Recently, Duato has solved this problem for a restricted class of adaptive routing algorithms. In this paper, a necessary and sufficient condition is proposed that ..."
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Cited by 17 (5 self)
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An important open problem in wormhole routing has been to find a necessary and sufficient condition for deadlockfree adaptive routing. Recently, Duato has solved this problem for a restricted class of adaptive routing algorithms. In this paper, a necessary and sufficient condition is proposed that can be used for any adaptive or nonadaptive routing algorithm for wormhole routing, as long as only local information is required for routing. The underlying proof technique introduces a new type of dependency graph, the channel waiting graph, which omits most channel dependencies that cannot be used to create a deadlock configuration. The necessary and sufficient condition can be applied in a straightforward manner to most routing algorithms. This is illustrated by proving deadlock freedom for a partially adaptive nonminimal mesh routing algorithm that does not require virtual channels and a fully adaptive minimal hypercube routing algorithm with two virtual channels per physical channel. B...
Optimal Fully Adaptive Wormhole Routing for Meshes
, 1993
"... A deadlockfree fully adaptive routing algorithm for 2D meshes which is optimal in the number of virtual channels required and in the number of restrictions placed on the use of these virtual channels is presented. The routing algorithm imposes less than half as many routing restrictions as any prev ..."
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Cited by 17 (8 self)
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A deadlockfree fully adaptive routing algorithm for 2D meshes which is optimal in the number of virtual channels required and in the number of restrictions placed on the use of these virtual channels is presented. The routing algorithm imposes less than half as many routing restrictions as any previous fully adaptive routing algorithm. It is also proved that, ignoring symmetry, this routing algorithm is the only fully adaptive routing algorithm that achieves both of these goals. The algorithm exploits the fact that for some adaptive routing algorithms, deadlock freedom is possible even when cycles are present in the channel dependency graph. The implementation of the routing algorithm requires relatively simple router control logic. The routing algorithm requires only the minimum number of virtual channels even when extended to arbitrary dimension meshes, yielding a dramatic reduction in the number of virtual channels needed to support fully adaptive routing. Compared to all previous algorithms which required an exponential number of virtual channels with the dimension of the mesh, the new algorithm requires only 4n  2 virtual channels for an ndimensional mesh.
A Universal Proof Technique for DeadlockFree Routing in Interconnection Networks
 In 7 th Annual ACM Symposium on Parallel Algorithms and Architectures
, 1995
"... An important open problem in interconnection network routing has been to characterize the conditions under which routing algorithms are deadlockfree. Although this problem has been resolved for restricted classes of routing algorithms, no general solution has been found. In this paper, we solve thi ..."
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Cited by 13 (4 self)
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An important open problem in interconnection network routing has been to characterize the conditions under which routing algorithms are deadlockfree. Although this problem has been resolved for restricted classes of routing algorithms, no general solution has been found. In this paper, we solve this problem by proving a necessary and sufficient condition that can be used for any interconnection network routing algorithm, as long as only local information is required for routing. Our proof technique is universal: it can be used with any switching technique that is not inherently deadlockfree. This includes switching techniques such as wormhole routing, storeandforward routing, and virtual cutthrough. The proof technique for the necessary and sufficient condition introduces a new type of dependency graph, the buffer waiting graph, which omits most dependencies that cannot be used to create a deadlock configuration. Our methodology is illustrated by proving deadlock freedom for a sto...
Optimal Fully Adaptive Minimal Wormhole Routing for Meshes
 Journal of Parallel and Distributed Computing
, 1995
"... A deadlockfree fully adaptive minimal routing algorithm for meshes that is optimal in the number of virtual channels required and in the number of restrictions placed on the use of these virtual channels is presented. It is also proved that, ignoring symmetry, this routing algorithm is the only fu ..."
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Cited by 11 (6 self)
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A deadlockfree fully adaptive minimal routing algorithm for meshes that is optimal in the number of virtual channels required and in the number of restrictions placed on the use of these virtual channels is presented. It is also proved that, ignoring symmetry, this routing algorithm is the only fully adaptive routing algorithm with uniform routers that achieves both of these goals. This new algorithm requires only 4n \Gamma 2 virtual channels for an ndimensional mesh. In addition, if more than the minimum number of virtual channels is available, the routing algorithm can use these additional channels with the fewest possible number of restrictions. The proofs are first presented for the 2D mesh and then generalized to ndimensional meshes. Keywords: wormhole routing, mesh architectures, routing algorithms, deadlock freedom, optimality. 1 Introduction Wormhole routing [6] has become the switching technique of choice in modern distributedmemory multiprocessors such as the Intel Par...