E. A. Varvarigos and D. P. Bertsekas, "Communication Algorithms for Isotropic Tasks in Hypercubes and Wraparound Meshes," Parallel Computing, Volumn 18, pages 12331257, 1992. 18  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... delay were considered in [5 9] For multihop networks such as rings, meshes, tori and hypercubes, the problem of scheduling AAPC assuming circuit switched routing was studied in [2,10,11] and the problem of scheduling arbitrary communications assuming store and forward routing was studied in [3, 12 15]. In this paper, we will investigate the problem of scheduling AAPC in WDM rings. Ring is a fairly common communication network architecture for local area networks (LAN) as well as multi processor systems [16 18] Work related to scheduling transmissions in rings has been reported in [2, 14, ....

E. Varvarigos and D. P. Bertsekas, "Communication algorithm for isotropic tasks in hypercubes and wraparound meshes," Parallel Computing 18, pp. 1233--1257, 1992.

....in one set. Thus the whole transfer can be completed in 2d CS(M) n e time units; by Fact 3. 2, this is no more than 2L and hence no more than 2T opt (M ) To tackle the case when M is an arbitrary n Theta n matrix, not necessarily perfect, we make use of the following result proved in [10]. Lemma 3.3 Given any nonnegative integer square matrix M , there is a square matrix Z such that M Z is a perfect matrix and CS(M Z) CS(M) The matrix Z simply indicates the dummy files that need to be transferred. The above result indicates that we can complete the transfer of all the ....

....matching R of the bipartite graph GW . For this, we use the algorithm of [4] In step 1, we invoke the subroutine FindPerfectMatrix to find a non negative square matrix E and a perfect non negative square matrix W with the same critical sum as M such that M E = W . The proof of Lemma 3. 3 given in [10] gives an implicit procedure to construct these matrices and we give an explicit efficient procedure below. The procedure we use is identical to the North West Corner (NWC) rule used in finding a feasible allocation in the transportation problem. In steps 11, 12, 13, and 14, f ij represents any ....

E. A. Varvarigos and D. P. Bertsekas, "Communication Algorithms for Isotropic Tasks in Hypercubes and Wraparound Meshes," Parallel Computing, to appear.

....11, 25] for circuit switched meshes, tori and hypercubes. A similar problem, called scheduling total (or complete) exchange, and its variations in which an arbitrary communication pattern needs to be scheduled, were studied for rings (unidirectional) in addition to meshes, tori and hypercubes in [2, 12, 26, 27, 30], where store and forward routing was assumed. Another similar problem, called scheduling all to all broadcasting, in which each node needs to broadcast the same packet to all other nodes, was studied for meshes, tori and hypercubes in [4,15,16] Note that only point to point, non multiplexed ....

E. Varvarigos and D.P. Bertsekas. Communication algorithms for isotropic tasks in hypercubes and wraparound meshes. Parallel Computing, 18:1233--1257, 1992.

.... delay were considered in [5 9] For multihop networks such as rings, meshes, tori and hypercubes, the problem of scheduling AAPC assuming circuit switched routing was studied in [2,10,11] and the problem of scheduling arbitrary communications assuming store and forward routing was studied in [3, 12 15]. In this paper, we will investigate the problem of scheduling AAPC in WDM rings. Ring is a fairly common communication network architecture for local area networks (LAN) as well as multi processor systems [16 18] Work related to scheduling transmissions in rings has been reported in [2, 14, ....

E. Varvarigos and D. P. Bertsekas, "Communication algorithm for isotropic tasks in hypercubes and wraparound meshes," Parallel Computing 18, pp. 1233--1257, 1992.

....for a non uniform but dense traffic pattern [1, 2] The schedule length is an important performance measure as it affects, for example, the throughput that can be achieved in the network. The problem of traffic scheduling in conventional networks has been studied extensively (see, for example, [1 8]) Traffic scheduling in broadcast and select WDM networks based on starcouplers has also received much attention (see, for example, 9 14] In this paper, we study the problem of scheduling all to all traffic in WDM rings. We choose the ring topology because it is fairly common for ....

E. Varvarigos and D. P. Bertsekas, "Communication algorithm for isotropic tasks in hypercubes and wraparound meshes," Parallel Computing 18, pp. 1233--1257, 1992.

....are symmetric with respect to any origin node. By considering also symmetric routing algorithms, one instance of isotropic tasks, the total exchange was reduced to a matrix decomposition problem, minimizing both completion time and average packet delay on the MIMD hypercube (and wraparound mesh) [319, 320]. While the hypercube definitions of isotropic tasks were based on XOR operations, those for the wraparound mesh were based on modular addition. Problem 14 Classify isotropic and nearly isotropic tasks in symmetric topologies. 4.3 Fault Tolerant Routing P faulty model. Assuming dynamic node ....

Varvarigos, E. A., and Bertsekas, D. P. Communication algorithms for isotropic tasks in hypercubes and wraparound meshes. Parallel Comput. 1992, 18, pp. 1233--1257.

....optimal slowdown. As a consequence, we obtain through emulation many effi cient algorithms for the MS network, which indicates its versatility. In particular, we obtain asymptotically optimal algorithms to execute basic communication tasks, such as the multinode broadcast and the total exchange [9, 13, 22, 28, 29], assuming either single port or all port communication. We also show that the multinode broadcast and the total exchange task cannot be performed in any interconnection networks with similar node degree in time that is asymptotically better by more than a constant factor than the time required ....

....k star onto the MS(l;n) network. The emulation result of Theorem 4.1 permits us to fi nd simple algorithms to execute certain prototype communication tasks in an MS network. Two basic communication tasks that arise often in applications are the multinode broadcast (MNB) and the total exchange (TE) [9, 28, 29]. In the MNB, each node has to broadcast a packet to all the other nodes of the network, while in the TE, each node has to send a different (personalized) packet to every other node of the network. Misic and Jovanovic [22] have proposed strictly optimal algorithms to execute both tasks in time k ....

Varvarigos, E.A. and D.P. Bertsekas, " Communication algorithms for isotropic tasks in hypercubes and wraparound meshes," Parallel Computing, Vol. 18, no. 11, Nov. 1992, pp. 1233-1257.

....also constitute a reference point for methods developed for the former type of networks. Algorithms to solve the total exchange problem for specific networks and under a variety of assumptions have appeared in many recent works, mostly concentrating in hypercubes and two dimensional tori (e.g. [22, 14, 2, 23]) Under the single port model we know of two optimal algorithms, in [3, pp. 81 83] for hypercubes, and in [19] for star graphs. In contrast, our results are applicable not only to one particular structure but rather provide a general procedure for solving the problem in any multidimensional ....

E. A. Varvarigos and D. P. Bertsekas, "Communication algorithms for isotropic tasks in hypercubes and wraparound meshes," Parallel Comput., Vol. 18, pp. 1233--1257, 1992.

....Japan. email: riro flab.fujitsu.co.jp. Since AAPC steps are so prevalent, many algorithms have been developed to perform AAPC efficiently, though implementations and performance numbers for these algorithms are hard to find. Most algorithms have concentrated on machines with a hypercube topology[16, 28, 26, 4]. More recent work has explored machines with a k ary n cube topology. In [28] Varvarigos and Bertekas propose a store and forward algorithm. Theoretically, this algorithm optimally uses network bandwidth. However, to utilize all network bandwidth, each node must be able to source and sink four ....

....have been developed to perform AAPC efficiently, though implementations and performance numbers for these algorithms are hard to find. Most algorithms have concentrated on machines with a hypercube topology[16, 28, 26, 4] More recent work has explored machines with a k ary n cube topology. In [28] Varvarigos and Bertekas propose a store and forward algorithm. Theoretically, this algorithm optimally uses network bandwidth. However, to utilize all network bandwidth, each node must be able to source and sink four messages simultaneously, i.e. have twice the memory bandwidth as incomingnetwork ....

[Article contains additional citation context not shown here]

VARVARIGOS, E. A., AND BERTSEKAS, D. P. Communication algorithms for isotropic tasks in hypercubes and wraparound meshes. Parallel Computing 18 (1992), 1233--1257.

....al. 1] presented an algorithm optimal for any fi. A detailed optimal scheduling algorithm has been presented by Edelman [2] who also implemented the algorithm on the Connection Machine. The algorithm uses indirect addressing, and has orbit lengths of order O(2 fi ) Varvarigos and Bertsekas [14] related AAPC on hypercubes and tori to a matrix decomposition problem. 2 All to all personalized communication on Boolean cubes 2.1 Preliminaries A Boolean n cube has N = 2 n nodes. Each node has n neighbors, which with the conventional binary addressing scheme correspond to the n different ....

Emmanouel A. Varvarigos and Dimitri P. Bertsekas. Communication algorithms for isotropic tasks in hypercubes and wraparound meshes. Technical report, Lab. of Information and Decision Systems, M.I.T., May 1990.

....total exchange problems. Total exchange is also known as multiscattering or all to all personalized communication. Algorithms to solve the problem for a number of networks under a variety of models assumptions have appeared in many recent works, mostly concentrating in hypercubes and tori (e.g. [18, 12, 3, 19]) Here we are going to follow the so called single port model in a store and forward network. Formally, our problem will be the distribution of distinct messages from every node to every other node subject to the following conditions: ffl only adjacent nodes can exchange messages, ffl a message ....

.... other networks, apart from Cayley ones, possess property (1) Is (1) satisfied in any node symmetric network As a last note, it is interesting to mention that total exchange can be viewed as a specific case of isotropic communication problems, as originally considered by Varvarigos and Bertsekas [19]. In our setting, a communication problem will be named isotropic if whenever node v 0 has k i 0 messages to send to node v i , node v x has k i messages to send to oe vx (v i ) for all i; x = 1; 2; n Gamma 1. In effect, all that is required for a communication problem to be isotropic ....

E. A. Varvarigos and D. P. Bertsekas, Communication algorithms for isotropic tasks in hypercubes and wraparound meshes, Parallel Comput., 18 (1992), pp. 1233-- 1257.

....is a reasonable assumption[Hin94] Since AAPC steps are so prevalent, many algorithms have been developed to perform AAPC efficiently, though implementations and performance numbers for these algorithms are hard to find. Most algorithms have concentrated on machines with a hypercube topology[JH89, VB92, Tak87, Bok91] More recent work has explored machines with a k ary n cube topology. In [VB92] Varvarigos and Bertekas propose a store and forward algorithm. Theoretically, this algorithm optimally uses network bandwidth. However, to utilize all network bandwidth, each node must be able to source ....

....developed to perform AAPC efficiently, though implementations and performance numbers for these algorithms are hard to find. Most algorithms have concentrated on machines with a hypercube topology[JH89, VB92, Tak87, Bok91] More recent work has explored machines with a k ary n cube topology. In [VB92] Varvarigos and Bertekas propose a store and forward algorithm. Theoretically, this algorithm optimally uses network bandwidth. However, to utilize all network bandwidth, each node must be able to source and sink four messages simultaneously, i.e. have twice the memory bandwidth as incoming ....

[Article contains additional citation context not shown here]

E. A. Varvarigos and D. P. Bertsekas. Communication algorithms for isotropic tasks in hypercubes and wraparound meshes. Parallel Computing, 18:1233--1257, 1992.

No context found.

Varvarigos, E.A. and D.P. Bertsekas, "Communication algorithms for isotropic tasks in hypercubes and wraparound meshes," Parallel Computing, vol. 18, no. 11, Nov. 1992, pp. 1233-1257.

..... c ) A 2 D layou t o f a 5 cube . lower bound N 2 =4 [which follows from the fact that the area of a graph is at least equal to B 2 [19, 25] where B = N=2 is the bisection width of a hypercube, or from Lemma 5. 1 of Section 5 since a total exchange task in a hypercube requires N=2 steps [20]. The proposed hypercube layout has maximum wire length N=3 o(N) which is (slightly) shorter than the best previous result [10] for hypercubes of (currently) practical sizes (e.g. N 2 14 = 16K) and has smaller area by a factor of 2:25 o(1) at the same time. Note that we can move the ....

Varvarigos, E.A. and D.P. Bertsekas, " Communication algorithms for isotropic tasks in hypercubes and wraparound meshes," Parallel Computing, vol. 18, no. 11, Nov. 1992, pp. 1233-1257.

....models. As a consequence, we obtain through emulation many effi cient algorithms for the MS network, thus indicating its versatility. In particular, we derive asymptotically optimal algorithms to execute basic communication tasks, such as the multinode broadcast (MNB) and the total exchange (TE) [12, 48, 49], assuming either single port or all port communication. We also show that the MNB and the TE tasks cannot be performed in an interconnection network of similar node degree in time that is asymptotically better by more than a constant factor than the time required in a balanced MS network, under ....

....the cost of implementation, and is also suitable for parallel systems that use wormhole routing. Many algorithms developed for the star graph fall into this category [38] Two basic communication tasks that arise often in applications are the multinode broadcast (MNB) and the total exchange (TE) [12, 27, 48, 49]. In the MNB each node has to broadcast a packet to all the other nodes of the network, while in the TE each node has to send a different (personalized) packet to every other node of the network. Mi si c and Jovanovi c [38] have proposed strictly optimal algorithms to execute both tasks in time ....

Varvarigos, E.A. and D.P. Bertsekas, " Communication algorithms for isotropic tasks in hypercubes and wraparound meshes," Parallel Computing, Vol. 18, no. 11, Nov. 1992, pp. 1233-1257.

No context found.

E. A. Varvarigos and D. P. Bertsekas, "Communication Algorithms for Isotropic Tasks in Hypercubes and Wraparound Meshes," Parallel Computing, Volumn 18, pages 12331257, 1992. 18

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