|
| This Article | ||
| ||
| Share | ||
| Bibliographic References | ||
| Add to: | ||
 Digg  Furl  Spurl  Blink  Simpy  Google  Del.icio.us  Y!MyWeb | ||
| Search | ||
| ||
| ASCII Text | x | ||
| Ben H.H. Juurlink, Jop F. Sibeyn, P.s. Rao, "Gossiping on Meshes and Tori," IEEE Transactions on Parallel and Distributed Systems, vol. 9, no. 6, pp. 513-525, June, 1998. | |||
| BibTex | x | ||
| @article{ 10.1109/71.689439, author = {Ben H.H. Juurlink and Jop F. Sibeyn and P.s. Rao}, title = {Gossiping on Meshes and Tori}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {9}, number = {6}, issn = {1045-9219}, year = {1998}, pages = {513-525}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.689439}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Parallel and Distributed Systems TI - Gossiping on Meshes and Tori IS - 6 SN - 1045-9219 SP513 EP525 EPD - 513-525 A1 - Ben H.H. Juurlink, A1 - Jop F. Sibeyn, A1 - P.s. Rao, PY - 1998 KW - Gossip KW - global communication KW - wormhole routing KW - mesh networks KW - torus networks. VL - 9 JA - IEEE Transactions on Parallel and Distributed Systems ER - | |||
Abstract—Algorithms for performing gossiping on one- and higher-dimensional meshes are presented. As a routing model, the practically important wormhole routing is assumed. We especially focus on the trade-off between the start-up time and the transmission time. For one-dimensional arrays and rings, we give a novel lower bound and an asymptotically optimal gossiping algorithm for all choices of the parameters involved. For two-dimensional meshes and tori, a simple algorithm composed of one-dimensional phases is presented. For an important range of packet and mesh sizes, it gives clear improvements upon previously developed algorithms. The algorithm is analyzed theoretically and the achieved improvements are also convincingly demonstrated by simulations, as well as an implementation on the Paragon. On the Paragon, our algorithm even outperforms the gossiping routine provided in the NX message-passing library. For higher-dimensional meshes, we give algorithms which are based on an interesting generalization of the notion of a diagonal. These algorithms are analyzed theoretically, as well as by simulation.
[1] M. Barnett, R. Littlefield, D.G. Payne, and R. van de Geijn, "On the Efficiency of Global Combine Algorithms for 2D Meshes with Wormhole Routing," J. Parallel and Distributed Computing, vol. 24, pp. 191-201, 1995.
[2] R. Berrendorf, H.C. Burg, U. Detert, R. Esser, M. Gerndt, and R. Knecht, "Intel Paragon XP/S—Architecture, Software Environment, and Performance," Technical Report KFA-ZAM-IB-9409, Forschungszentrum Jülich GmbH, 1994.
[3] O. Delmas and S. Perennes, "Circuit-Switched Gossiping in 3-Dimensional Torus Networks," Proc. Second Euro-Par Conf., LNCS vol. 1123, pp. 370-373, 1996.
[4] P. Fraigniaud and J. Peters, "Structured Communication in Torus Networks," Proc. 28th Ann. Hawaii Int'l Conf. System Sciences, pp. 584-593, 1995.
[5] Y. Huang and P.K. McKinley, "An Adaptive Global Reduction Algorithm for Wormhole-Routed 2D Mesh Networks," Proc. Seventh Symp. Parallel and Distributed Processing, pp. 114-121, 1995.
[6] K. Hwang, Advanced Computer Architecture: Parallelism, Scalability, Programmability. McGraw-Hill, 1993.
[7] B.H.H. Juurlink, "Experimental Validation of Parallel Computation Models on the Intel Paragon," Proc. 12th Int'l Parallel Processing Symp. and Ninth Symp. Parallel and Distributed Processing, pp. 492-497, 1998.
[8] M. Kaufmann and J.F. Sibeyn, "Randomized Multipacket Routing and Sorting on Meshes," Algorithmica, vol. 17, pp. 224-244, 1997.
[9] D.W. Krumme, “Fast Gossiping for the Hypercube,” SIAM J. Computing, vol. 21, no. 2, pp. 365-380, Apr. 1992.
[10] A.B. Maccabe, K.S. McCurley, R. Riesen, and S.R. Wheat, "SUNMOS for the Intel Paragon: A Brief User's Guide," Proc. Intel Supercomputer Users Group Ann. North Am. Users Conf., 1993.
[11] J.E. Marsden and A.J. Tromba, Vector Calculus. W.H. Freeman and Company, 1981.
[12] L.M. Ni and P.K. McKinley, "A Survey of Wormhole Routing Techniques in Direct Networks," Computer, vol. 26, no. 2, pp. 62-76, Feb. 1993.
[13] J. Peters and M. Syska, "Circuit-Switched Broadcasting in Torus Networks," IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 3, pp. 246-255, 1996.
[14] S. Rajasekaran, “$k$-$k$Routing,$k$-$k$Sorting, and Cut-through Routing on the Mesh,” J. Algorithms, vol. 19, no. 3, pp. 361–382, 1995.
[15] J.H. Reif and L.G. Valiant, "A Logarithmic Time Sort for Linear Size Networks," J. ACM, vol. 34, pp. 60-76, Jan. 1987.
[16] P.S. Rao and G. Mouney, "Data Communications in Parallel Block Predictor-Corrector Methods for solving ODEs," Technical Report LAAS-CNRS, France, 1995.
[17] N.S. Sundar, D.N. Jayasimha, D.K. Panda, and P. Sadayappan, "Hybrid Algorithms for Complete Exchange in 2D Meshes," Proc. Int'l Conf. Supercomputing, 1996.
[18] Y.-C. Tseng, T.-H. Lin, S. Gupta, and D.K. Panda, “Bandwidth-Optimal Complete Exchange on Wormhole Routed 2D/3D Torus Networks: A Diagonal-Propagation Approach,” IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 4, pp. 380-396, Apr. 1997.