A fast parallel algorithm for routing in permutation networks

Lev, G.; Valiant, Leslie G.; Pippenger, Nicholas

doi:10.1109/tc.1981.6312171

Cited by 218 publications

(53 citation statements)

References 19 publications

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“…In order to speed up routing, parallel algorithms must be used. For rearrangeable 3-stage Clos networks, the best parallel time complexity is O(log 2 N ) if the number of middle stage modules is a power of 2 [8]. This result is also reported in [11,12] in different forms.…”

Section: Introductionsupporting

confidence: 63%

A practical fast parallel routing architecture for Clos networks

Zheng

Gumaste

2006

Proceedings of the 2006 ACM/IEEE Symposium on Architecture for Networking and Communications Systems

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Clos networks are an important class of switching networks due to their modular structure and much lower cost compared with crossbars. For routing I/O permutations of Clos networks, sequential routing algorithms are too slow, and all known parallel algorithms are not practical. We present the algorithm-hardware codesign of a unified fast parallel routing architecture called distributed pipeline routing (DPR) architecture for rearrangeable nonblocking and strictly nonblocking Clos networks. The DPR architecture uses a linear interconnection structure and processing elements that performs only shift and logic AND operations. We show that a DPR architecture can route any permutation in rearrangeable nonblocking and strictly nonblocking Clos networks in O( √ N ) time. The same architecture can be used to carry out control of any group of connection/disconnection requests for strictly nonblocking Clos networks in O( √ N ) time. Several speeding-up techniques are also presented. This architecture is applicable to packet and circuit switches of practical sizes.

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Section: Introductionsupporting

confidence: 63%

A practical fast parallel routing architecture for Clos networks

Zheng

Gumaste

2006

Proceedings of the 2006 ACM/IEEE Symposium on Architecture for Networking and Communications Systems

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“…Prakash et al [25] proposed an 4 6 5 8 7 ¥ 9 ' @ B A 1 D C parallel algorithm based on pointer jumping for scheduling packets in the SMS architecture; as in [7], this router emulates an output-queued router. However, the algorithm is impractical to implement, since it uses the NC algorithm in [17] to edge-color bipartite graphs. Chuang et al [7] have shown that a router with buffering at both the input and output ports can emulate an output-queued router by performing 2 reads and 2 writes on the input and output buffers, respectively, and running the switch fabric twice in a cycle.…”

Section: Prior Work On Router Schedulingmentioning

confidence: 99%

A near optimal scheduler for switch-memory-switch routers

Aziz¹,

Prakash²,

Ramachandra³

2003

Proceedings of the Fifteenth Annual ACM Symposium on Parallel Algorithms and Architectures - SPAA '03

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Routers are ubiquitous in modern computing, appearing in wide-area networks, multiprocessor servers, and data storage systems. Modern routers achieve high performance by solving computationally intensive tasks using custom hardware. One of the most challenging problems in designing a high-end router is scheduling the transfer of packets from inputs to outputs.We present a simple and near optimal randomized parallel scheduling algorithm for scheduling packets in routers based on the Switch-Memory-Switch (SMS) architecture, which emulates 'output queuing' by using a collection of small memories within the switch to buffer packets, and which forms the basis of the fastest routers in use today. Specifically, for a router with inputs and outputs, our algorithm computes the schedule inrounds, where a round is a communication of a few bits between input ports and memory together with simple local computation at the inputs and memory. Furthermore, by using andeep pipeline at each input, our algorithm computes the schedule in a constant number of rounds. Our pipelined algorithm is quite simple and achieves optimal (i.e., constant) throughput with a tiny ¡ £ ¢ ¤ § ¦ © delay. We show that the total amount of buffer memory required by our algorithm is close to the minimum required. We also show that the number of buffer memories is within an is the minimum number of memories needed under adversarial placement of packets. Furthermore we show that the number of extra memories that we use over the minimum of that is required in the offline version, is within a constant factor of the minimum required by any on-line scheduler, even if that scheduler is allowed to fail occasionally.Our scheduling algorithm is randomized and works with high probability in . We also prove that it has the 'self-stabilizing' property, i.e., it resumes its normal behavior if occasional lapses occur due to the probabilistic nature of the algorithm.

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“…In addition-and this seems not to be widely realized-she also gave an NC 4 algorithm for finding a maximum matching (henceforth MAXMLMATCH) in any regular bipartite graph by means of an NC 4 edge coloring algorithm for this family. The bound was improved to NC 2 in [156]. The complexity for general regular graphs remains open, although see [157].…”

Section: Matching In Parallelmentioning

confidence: 99%

Matching and Vertex Packing: How Hard Are They?

Plummer¹

1991

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ECE 21 ABSTACTFEB 19920Two of the most well-known problems in graph theory are: D (a) Find a maximum matching (or perfect matching, if one exists), and (b) Find a maximum independent set of vertices.The first problem-usually called the matching problem-is known to have a polynomial algorithm; the second-often called the vertex packing problem-is known to be NP-complete. However, many graph theorists-especially those who do not deal much with complexity of algorithms-know little more about the complexity issues associated with these two problems than these two basic facts.What is not so widely known within the graph theory community is that these two problems have motivated a great deal of recent activity in the area of algorithms and their complexity. Of course it is not known whether or not P = NP, but most workers in the area currently believe that equality is unlikely to hold. Motivated by this belief, a number of people have studied variations of both matching and vertex packing with the general theme being two-fold. On the one hand, one can add various side conditions to the matching problem and study the complexity-both sequential and parallel-of the resulting --problems. On the other hand, one can investigate certain large and interesting classes of graphs trying to prove that for these classes the vertex packing problem has a polynomial solution.Each branch of this two-pronged attack has yielded both interesting theorems and 0 perplexing unsolved problems. This paper will survey this work. I Introduction and Background: The two fundamental ProblemsIn this paper, graphs will be assumed to be connected, undirected and will have no multiple edges or loops. A matching is any set of independent edges; i.e., no two have a vertex in common. A maximal matching is a matching not properly contained in any other matching. A maximum matching is one of largest cardinality. A perfect matching (sometimes called a 1-factor) in a graph G is a matching which covers all vertices of G. A set of vertices S C V(G) is independent if no two vertices of S are adjacent. An * work supported by ONR Contract #N00014-85-K-0488, #N00014-91-J-1142 and Laboratoire de Recherche en Informatique, CNRS, Univ. Paris Sud ___ 1 ir P'zblic release and sale; its ) I di-ziutIon is unlimited. independent set S is maximal if it is not a proper subset of any other independent set and maximum if it is an independent set of largest cardinality.So far, then, maximal and maximum matchings and independent sets are quite analogous; matchings corresponding to sets of edges and independent sets corresponding to sets of vertices. To be sure, they are related. A (maximal, maximum) matching in a graph G corresponds to a (maximal, maximum) independent set in the line graph L(G). But we shall soon see that the concepts quickly diverge in difficulty.First, however, let us note that matching and vertex packing remain closely related, at least in the computational sense, if one considers the class of bipartite graphs. Historically speaking, it was this class of gra...

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A fast parallel algorithm for routing in permutation networks

Cited by 218 publications

References 19 publications

A practical fast parallel routing architecture for Clos networks

A practical fast parallel routing architecture for Clos networks

A near optimal scheduler for switch-memory-switch routers

Matching and Vertex Packing: How Hard Are They?

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