T. Szymanski, Hypermeshes: optical interconnection networks for parallel computing, J. Parallel Distrib. Comput. 26 (1995) 1--23.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in the electrical domain. The primary in uence on the development of optical optoelectronic interconnection networks has come from topology and metrics. Some of the electrical based topologies that have contributed to optical based interconnection networks are: the fat tree [4] mesh crossbar [10], omega network [1] hypercube [5] and mesh and hypercube hybrid [6] Performance metrics from the electrical domain have also been frequently used to characterize the goodness of optical optoelectronic interconnection networks. The network diameter has frequently been used for comparison ....

T. H. Szymanski, \Hypermeshes: Optical interconnection networks for parallel computing," Jounal of Parallel and Distributed Computing, vol. 26, pp. 1-23, 1995.

.... The interconnection network [46] might be a shared medium network (such as Ethernet, Token Ring) a direct network (such as mesh, torus) an indirect network (multistage interconnection network such as IBM SP [112] or irregular such as Myrinet [23] or a hybrid network (such as hypermesh) [117]. The routing algorithm determines which routes messages should follow through the network to reach their destinations. There are many different routing algorithms with different guarantees and performance such as Duato s adaptive routing [47] Glass and NI s turn model routing [56] and ....

T. Szymanski, "Hypermeshes: Optical Interconnection Networks for Parallel Computing ", Journal of Parallel and Distributed Computing, 26, 1995, pp. 1-35.

....is not a useful tool to study routing algorithms and deadlocks in a k ary m way network. c3 c6 c0 c1 c2 c0 P 0 P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 c 3 c 4 c 5 c 6 c 8 c 0 c 1 c 2 c 7 Figure 4: Graph model of a 3 ary 5 way torus Examples of bus interconnection networks are the hypermesh [12], hypergrid (hypertorus) 7] and hyperbus [2] In a hypermesh, each node is connected to all the nodes in each dimension through a bus. If k is the number of nodes along each of the n dimensions then nk is the number of buses in the network. Each node is connected to n buses and the network ....

T. Szymanski, Hypermeshes: Optical interconnection networks for parallel processing, Journal of Parallel and Distributed Computing, vol. 26, pages 1-23, January 1995.

....one since each processor is directly connected to every other processor, and has a maximal bisection bandwidth. Another advantage of a crossbar switch is that it can be used as the basis of other larger interconnection networks including multistage networks and hierarchical networks . 20] 21][22] For these reasons, several parallel processing architectures have been designed with crossbar interconnects. The primary disadvantage of a crossbar network is the complexity and cost of implementation. Electronic crossbar networks require a wire or set of wires from each processor to every other ....

T. Szymanski, "Hypermeshes: Optical interconnection networks for parallel computing," J. of Parallel and distributed computing, vol. 26, pp. 1-23, 1995.

....Therefore, the granularity of size scaling following the fixed n rule is 2 n (2w 1) 2(N w) 2 n . Note that the granularity of size scaling using the fixed w rule is O(N) while, for the fixed n rule, it is O(N w) SMLH is competitive with other networks in this smooth scalability property [33]. Fig. 3. An SMLH(w = 3, n = 3) 72 nodes) interconnection. This SMLH network can be constructed by adding hypercube modules along a row and a column. 502 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 9, NO. 5, MAY 1998 2.3.4 Average Message Distance The average message distance ....

....function is being applied can be side stepped by forwarding the message to the neighboring hypercube via a SMN operation, as shown in Fig. 3. In general, for an SMLH(w, n) network, n two hop rerouting schemes are available to bypass a faulty link which is competitive with other networks [12] [33]. 3COMPARISONS OF SMLH WITH POPULAR NETWORKS In this section, we compare the SMLH network with existing, well known topologies. These include the Binary Hypercube (BHC) 8] the Generalized Hypercube (GHC) 12] the Torus [34] the Spanning Bus Hypercube (SBH) 21] the Hierarchical Cubic ....

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# T. Szymanski, "Hypermeshes: Optical Interconnection Networks for Parallel Computing," J. Parallel and Distribted Computing, vol. 26, pp. 1--23, 1995.

.... One is to implement traditional, and design new novel, point topoint interconnection networks [18] but utilizing the advantages of the new emerging optical technologies to overcome the constraints of metal based communication, while the second direction is to design new interconnection networks [4][27] based on the constraints of optical devices, such as optical passive star coupler (OPS) interconnection networks which can be modeled by hypergraphs. Along the first direction, we introduce a complete network using a reconfigurable free space optical interconnect. Free space optical ....

T. Szymanski, "Hypermeshes: Optical Interconnection Networks for Parallel Computing," Journal of Parallel and Distributed Computing, 26, 1995, pp. 1-35

....of M. Dilation is the the maximum length of an image path b(e) for every edge e of G. Congestion is the maximum number of image paths including an edge e 0 for every edge e 0 of M. Meanwhile, hypermeshes have been given much attention as a graph model of a versatile parallel architecture [16, 19]. A hypermesh is obtained from a mesh by replacing each linear connection with one hyper edge. A hyper edge is an edge without the restriction that an edge should connect only two nodes. Figure 1 shows an example of a 4 Theta 4 hypermesh where each hyper edge is represented as a bus. 2 1 0 3 Bus ....

....that an edge should connect only two nodes. Figure 1 shows an example of a 4 Theta 4 hypermesh where each hyper edge is represented as a bus. 2 1 0 3 Bus 3 1 2 Processor 2 2 1 0 3 3 0 1 0 Figure 1: A 4 Theta 4 hypermesh Several practical implementations of the hypermeshes have been suggested in [7, 10, 16, 19]. The hypermesh is especially attractive when it is combined with optical buses because the optical buses offer high communication bandwidth. Optical buses provide multiple channels on the same bus by wavelength division multiplexing [4] or allow message pipelining by space time multiplexing [10, ....

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T. Szymanski, "Hypermeshes: optical interconnection networks for parallel processing," J. Parallel Distrib. Comput., Vol. 26, pp. 1-26, 1995.

....the first and third embedding is one if s = 2 k Gamma 1 for some integer k, otherwise, less than two. The expansion of the second embedding is 2 ffl(s) where ffl(s) 2 log(s 1) 2) s 1) 1 Introduction Hypermeshes have been given much attention as versatile interconnection networks [12, 13, 16]. A hypermesh is obtained from a mesh by replacing Dept. of Computer Science, Korea Advanced Institute of Science and Technology, Taejon 305 701, Korea, fsykim, kychwag jupiter.kaist.ac.kr, Tel: 82 42 869 f3568,3513g, Fax: 82 42 869 3510 y Dept. of Computer Engineering, Pukyong National ....

....the restriction that an edge should connect only two nodes. For example, an 8 Theta 8 hypermesh is shown in Figure 2. In this figure, each node is represented as ffl or ffi and each hyperedge is represented as a solid or hollow line. Hypermeshes have great advantages in many network metrics [12, 13, 16]. First, their diameter grows slowly with the number of nodes, compared with most existing networks. Second, they can host parallel algorithms that map naturally to a variety of more restricted topologies, such as hypercubes, binary trees, and meshes. Third, they can realize, in one pass and ....

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T. Szymanski, "Hypermeshes: optical interconnection networks for parallel computing," J. Parallel Distrib. Comput., Vol. 26, pp. 1-23, 1995.

....nodes, instead of only two nodes. As for graphs, a hyperedge represents a communication means; a message sent on a hyperedge can be read by all nodes in that hyperedge. In the case of WDM passive star networks, a speci c wavelength (or channel) can be seen as a logical bus and, as pointed out in [15], a logical bus can be modeled by a hyperedge (see Figure 3 for the hypergraph representation of the multi hop network depicted in Figure 2) To make this idea clear, let stations A, B, and C form a hyperedge (i.e. share a channel) and the channel speed be v Mbit s. Then, if A has v Mbits of ....

.... ( 5, 8] In this paper we present a comparative study of three hypergraphbased networks namely the stack ring, the stack torus, and the hypertorus ( 5] and two very well known graphbased 1 Although intuitive, it seems that the term hyperedge has been rst used in an early version of [15]. topologies namely the hypercube and the twodimensional torus ( 7] It is clear that one tomany topologies would be much more eOEcient than point to point topologies when implementing multicast (i.e. one to many) communications. However, since many applications require one to one ....

T. Szymanski. Hypermeshes: Optical Interconnection Networks for Parallel Computing. Journal of Parallel and Distributed Computing, 26:123, 1995.

....less than two. The expansion of the second embedding is 2 ffl(s) where ffl(s) 2 log(s 1) 2) s 1) Keywords: Graph embedding; Hypermesh; Butterfly; Alignment cost; Congestion; Expansion 1. Introduction Hypermeshes have been given much attention as versatile interconnection networks [1,2,3]. A hypermesh is obtained from a mesh by replacing each linear connection with a hyperedge. A hyperedge is an edge without the restriction that an edge should connect only two nodes. For example, an 8 Theta 8 hypermesh is shown in Figure 1 (a) In this figure, each node is represented as ffl or ....

....2,2 6,3 7,3 5,1 1,0 4,3 5,3 3,1 2,0 1,2 7,0 0,1 1,1 0,3 4,2 6,1 0,2 1,3 0,0 3,2 5,3 6,3 7,3 4,3 7,0 6,0 5,0 4,0 4,1 level 0 1 2 3 3,0 0,2 0,3 1,3 2,3 3,3 1,2 2,0 1,0 0,0 1,1 0,1 Gamma(6) a) b) Fig. 1. Hypermesh M(8; 8) and butterfly B(3) Hypermeshes have great advantages in many network metrics [1,2,3]. First, their diameter grows slowly with the number of nodes, compared with most existing networks. Second, they can host parallel algorithms that map naturally to a variety of more restricted topologies, such as hypercubes, binary trees, and meshes. Third, they can realize, in one pass and ....

[Article contains additional citation context not shown here]

T. Szymanski, Hypermeshes: optical interconnection networks for parallel computing, J. Parallel Distrib. Comput. 26 (1995) 1--23.

....at each hop. Other examples may be found in [17 19] Virtual point to point architectures [20 22] map a logical topology typically to a star coupled network via wavelength , spatial , and or time multiplexing. A formal model of the construction of large WDM based networks is considered in [23 25], 26, 27] devised WDM based architectures that include space and time multiplexing to support scalability and reduce the design constraints (number of channels and device tuning speed) and [28] considered power limitations of typical channel configurations. Media access protocols developed for ....

....m = C but must be extended in a time division fashion when m C. An advantage of slot extension is immediate detection of a collision, but system performance degrades as the propagation delay increases and when the processing latencies are significant relative to the packet transmission time [25,37]. Slot extension is used here since the propagation delay in an optical backplane for processor interconnection is much less than in a general local area network environment. Interleaved TDMA: I TDMA avoids collisions and the complexity of supporting acknowledgments and retransmissions by time ....

T. Szymanski, "Hypermeshes: Optical interconnection networks for parallel computation," Journal of Parallel and Distributed Computing, Under Review, 1993.

....be considered. Dynamic routing forms a reasonable network performance model [10] In dynamic routing, each network node generates packets at a fixed rate, assigning to each packet an independently chosen random destination. All packets must then be routed in parallel to their final destinations [17]. Good approximations to empirical data have been obtained for dynamic routing on the binary hypercube, using shortest path routing [1] In this paper, we propose a new model for multicast communication. The term multicast refers to the transmission of data from one source to a set of destinations ....

T. Szymanski. Hypermeshes: optical interconnection networks for parallel computin. J. Parallel Distrib. Comput., 26(1):1--23, April 1995.

....and the hyper ones constructed with simple pieces combined by a cartesian product operation. These pieces are the hyperpaths and the hyperrings, that will be defined first. We refer the interested reader to [5, 6, 7] 1 Although intuitive, it seems that the term hyperedge was first used in [12] 2.1 Hypergraphs 2.2 Hyperpath Hyperring Definition 1 (Hyperpath P n;m (V; E) A hyperpath of size n and order m is defined in [5] as a hypergraph P n;m (V; E) such that: V = f0; nm Gamma 1g e 2 E ( e = fv 1 ; vm ; v 0 1 ; v 0 m g where 8 : v i = v j mod ....

T. Szymanski. Hypermeshes: Optical interconnection networks for parallel computing. Journal of Parallel and Distributed Computing, 26:1--23, 1995.

....one to many WDM lightwave networks are designed from hypergraph models, and thus called hypertopologies. As an example, Figure 1 shows a hyperring (to be defined in the next section) and its implementation in a wavelength multiplexed optical bus. Another approach for hypergraph models was used in [21], where the hypermesh architecture was studied. In this case, hypergraph edges were used to model optical cross bars. 1 2 5 9 10 3 7 11 6 8 4 0 f 3 1 0 2 3 4 5 6 7 8 9 f f f f f f f f f f f f f f f f f 0 0 2 0 0 2 2 0 1 2 0 1 2 2 1 1 1 1 11 10 0 2 1 3 f f f f f 3 3 3 3 3 Figure 1: A hyperring ....

....For the sake of completeness, we present in the following the hypertopologies to be compared in Sections 3 and 4. We refer the interested reader to [2, 6, 7, 10, 20] where details about them can be found. 1 Although intuitive, it seems that the term hyperedge was first used in [21]. 2.1 Hyperpath Hyperring Definition 1 A hyperpath (see Figure ) of size n and order m is a hypergraph P n;m (V; E) such that V = f0; nm Gamma 1g, and e 2 E ( e = fv 1 ; vm ; v 0 1 ; v 0 m g, where v i = v j mod n; v 0 i = v 0 j mod n; and v i = v 0 i ....

T. Szymanski. Hypermeshes: Optical Interconnection Networks for Parallel Computing. Journal of Parallel and Distributed Computing, 26:1--23, 1995.

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T. Szymanski, Hypermeshes: optical interconnection networks for parallel computing, J. Parallel Distrib. Comput. 26 (1995) 1--23.

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Szymanski, T. (1995) Hyper-meshes: Optical interconnection networks for parallel processing. J. Parallel Distributed Computing, 26, 1--26.

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T. Szymanski. Hypermeshes optical interconnection networks for parallel computing. J. of Par. and Distr. Comp., 26:123, April 1996.

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T. Szymanski, Hypermeshes: Optical interconnection networks for parallel processing, Journal of Parallel and Distributed Computing, vol. 26, pages 1-23, January 1995.

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