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Deterministic manytomany hot potato routing
 IEEE Transactions on Parallel and Distributed Systems
, 1997
"... We consider algorithms for manytomany hot potato routing. In hot potato (deflection) routing a packet cannot be buffered, and is therefore always moving until it reaches its destination. We give optimal and nearly optimal deterministic algorithms for manytomany packet routing in commonly occurrin ..."
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We consider algorithms for manytomany hot potato routing. In hot potato (deflection) routing a packet cannot be buffered, and is therefore always moving until it reaches its destination. We give optimal and nearly optimal deterministic algorithms for manytomany packet routing in commonly occurring networks such as the hypercube, meshes and tori of various dimensions and sizes, trees and hypercubic networks such as the butterfly. All these algorithms are analyzed using a charging scheme that may be applicable to other algorithms as well. Moreover, all bounds hold in a dynamic setting in which packets can be injected at arbitrary times.
Potential Function Analysis of Greedy HotPotato Routing (Extended Abstract)
 Theory of Computing Systems
, 1994
"... Amir BenDor Shai Halevi y Assaf Schuster z January 21, 1994 Abstract In this work we study the problem of packet routing in synchronous networks of processors, in which at most one packet can traverse any communication link in each time step. We consider a class of algorithms known as hotpo ..."
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Cited by 30 (2 self)
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Amir BenDor Shai Halevi y Assaf Schuster z January 21, 1994 Abstract In this work we study the problem of packet routing in synchronous networks of processors, in which at most one packet can traverse any communication link in each time step. We consider a class of algorithms known as hotpotato or deflection routing algorithms. The important characteristic of these algorithms is that they use no buffer space for storing delayed packets. Each packet, unless already arrived to its destination, must leave the processor at the step following its arrival. The main advantage in hotpotato routing is that there is no need to store delayed packets in the processors, and therefore, the processors can be much simpler, and contain less hardware. This work is concerned with greedy routing, in which a packet is bound to use an outgoing link in the direction of its destination, whenever such a link is available. In this way, greediness guarantees that, unless some global congestion forbids...
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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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...
Routing in Multihop Packet Switching Networks: Gbps Challenge
 IEEE Network
, 1995
"... The paper is a survey of networking solutions that have been proposed for highspeed packetswitched applications. Using these solutions as examples, we identify the specific problems resulting from very high transmission rates and explain how these problems influence the design of highspeed networ ..."
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Cited by 25 (1 self)
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The paper is a survey of networking solutions that have been proposed for highspeed packetswitched applications. Using these solutions as examples, we identify the specific problems resulting from very high transmission rates and explain how these problems influence the design of highspeed networks and protocols. We conclude that the solutions based on deflection routing are the most promising ones and we suggest a number of directions for their evolution. 1 Introduction Not so long ago, computer networks with high transmission rates (e.g. several Mb/s) were naturally confined to local domains. Although such (and higher) transmission rates were available in telephony on long distances, they were used on a pointtopoint basis. Concepts of highlyconnected fast networks spanning geographical areas larger than the acreage typically covered by a single institution are relatively new and, besides the emerging atm technology, there are no standard commercially available solutions that c...
Minimal Adaptive Routing on the Mesh with Bounded Queue Size
, 1994
"... An adaptive routing algorithm is one in which the path a packet takes from its source to its destination may depend on other packets it encounters. Such algorithms potentially avoid network bottlenecks by routing packets around "hot spots." Minimal adaptive routing algorithms have the a ..."
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Cited by 10 (4 self)
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An adaptive routing algorithm is one in which the path a packet takes from its source to its destination may depend on other packets it encounters. Such algorithms potentially avoid network bottlenecks by routing packets around "hot spots." Minimal adaptive routing algorithms have the additional advantage that the path each packet takes is a shortest one. For a large class of minimal adaptive routing algorithms, we present an \Omega# n 2 =k 2 ) bound on the worst case time to route a static permutation of packets on an n 2 n mesh or torus with nodes that can hold up to k 1 packets each. This is the first nontrivial lower bound on adaptive routing algorithms. The argument extends to more general routing problems, such as the hh routing problem. It also extends to a large class of dimension order routing algorithms, yielding an \Omega# n 2 =k) time bound. To complement these lower bounds, we present two upper bounds. One is an O(n 2 =k) time dimension order routing...
ManytoMany Routing on Trees via Matchings
, 1996
"... In this paper we present an extensive study of manytomany routing on trees under the matching routing model. Our study includes online and offline algorithms. We present an asymptotically optimal online algorithm which routes k packets to their destination within d(k \Gamma 1) + d \Delta dist r ..."
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In this paper we present an extensive study of manytomany routing on trees under the matching routing model. Our study includes online and offline algorithms. We present an asymptotically optimal online algorithm which routes k packets to their destination within d(k \Gamma 1) + d \Delta dist routing steps, where d is the degree of tree T on which the routing takes place and dist is the maximum distance any packet has to travel. We also present an offline algorithm that solves the same problem within 2(k \Gamma 1)+dist steps. The analysis of our algorithms is based on the establishment of a close relationship between the matching and the hotpotato routing models that allows us to apply tools which were previously used exclusively in the analysis of hotpotato routing.
A Lower Bound for Nearly Minimal Adaptive and Hot Potato Algorithms
"... Recently, Chinn, Leighton, and Tompa [10] presented lower bounds for storeandforward permutation routing algorithms on the n × n mesh with bounded buffer size and where a packet must take a shortest (or minimal) path to its destination. We extend their analysis to algorithms that are nea ..."
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Cited by 7 (1 self)
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Recently, Chinn, Leighton, and Tompa [10] presented lower bounds for storeandforward permutation routing algorithms on the n &times; n mesh with bounded buffer size and where a packet must take a shortest (or minimal) path to its destination. We extend their analysis to algorithms that are nearly minimal. We also apply this technique to the domain of hot potato algorithms, where there is no storage of packets and the shortest path to a destination is not assumed (and is in general impossible). We show that "natural" variants and "improvements" of several algorithms in the literature perform poorly in the worst case. As a result, we identify algorithmic features that are undesirable for worst case hot potato permutation routing. Recent works in hot potato routing have tried to define simple and greedy classes of algorithms. We show that when an algorithm is too simple and too greedy, its performance in routing permutations is poor in the worst case. Specifically, the technique of [10] ...
Experimental evaluation of hotpotato routing algorithms on 2dimensional processor arrays
 In EUROPAR: Parallel Processing, 6th International EUROPAR Conference
, 2000
"... Abstract. In this paper we consider the problem of routing packets in twodimensional torusconnected processor arrays. We describe the implementation of four hotpotato routing algorithms and study their performance by experimentation. The algorithms are either greedy in the sense that packets try ..."
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Abstract. In this paper we consider the problem of routing packets in twodimensional torusconnected processor arrays. We describe the implementation of four hotpotato routing algorithms and study their performance by experimentation. The algorithms are either greedy in the sense that packets try to move towards their destination by adaptively using a shortest path, or have the property that the path traversed by any packet approximates the path traversed by the greedy routing algorithm in the storeandforward model. Moreover, they are simple and were implemented according to the one or twopass scheme. In our experiments, we consider the static case of the routing problem where we study permutation and random destination input instances as well as the dynamic case of the problem under the stochastic model for the continuous generation of packets. Our experimental results demonstrate that, although the running time of all the algorithms is close to the optimal for static routing problems, heavy traffic may influence differently the performance of each algorithm in the dynamic case.
The data vortex, an all optical path multicomputer interconnection network
 IEEE Trans. Parallel Distrib. Syst
, 2007
"... Abstract—All optical path interconnection networks employing dense wavelength division multiplexing can provide vast improvements in supercomputer performance. However, the lack of efficient optical buffering requires investigation of new topologies and routing techniques. This paper introduces and ..."
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Abstract—All optical path interconnection networks employing dense wavelength division multiplexing can provide vast improvements in supercomputer performance. However, the lack of efficient optical buffering requires investigation of new topologies and routing techniques. This paper introduces and evaluates the Data Vortex optical switching architecture which uses cylindrical routing paths as a packet buffering alternative. In addition, the impact of the number of angles on the overall network performance is studied through simulation. Using optimal topology configurations, the Data Vortex is compared to two existing switching architectures—butterfly and omega networks. The three networks are compared in terms of throughput, accepted traffic ratio, and average packet latency. The Data Vortex is shown to exhibit comparable latency and a higher acceptance rate (2x at 50 percent load) than the butterfly and omega topologies. Index Terms—Optical switch fabrics, optical switching, photonic packet switch, data vortex switch architecture, packet switching. Ç 1
HotPotato Routing on MultiDimensional Tori
 LECTURE NOTES IN COMPUTER SCIENCE
, 1995
"... . We consider the hotpotato routing problem. The striking feature of this form of packet routing is that there are no buffers at the nodes. Thus packets are always moving. A probabilistic hotpotato routing protocol is presented that routes random functions on the (n; d)torus. If at most d 88 n ..."
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Cited by 5 (2 self)
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. We consider the hotpotato routing problem. The striking feature of this form of packet routing is that there are no buffers at the nodes. Thus packets are always moving. A probabilistic hotpotato routing protocol is presented that routes random functions on the (n; d)torus. If at most d 88 n d packets, evenly distributed among the processors, have to be routed, they all have reached their destinations in dn + O \Gamma d 3 log n \Delta steps, with high probability, if 3 d = O (n ffl ) with ffl 2 \Gamma 0; 1 2 \Delta . This improves upon previous results where similar time bounds are only obtained for constant d and n d packets.