Publication 1996 Issue No. 11 - November Abstract - Fast Gossiping on Mesh-Bus Computers
Fast Gossiping on Mesh-Bus Computers
November 1996 (vol. 45 no. 11)
pp. 1326-1330
 ASCII Text x Satoshi Fujita, Masafumi Yamashita, "Fast Gossiping on Mesh-Bus Computers," IEEE Transactions on Computers, vol. 45, no. 11, pp. 1326-1330, November, 1996.
 BibTex x @article{ 10.1109/12.544491,author = {Satoshi Fujita and Masafumi Yamashita},title = {Fast Gossiping on Mesh-Bus Computers},journal ={IEEE Transactions on Computers},volume = {45},number = {11},issn = {0018-9340},year = {1996},pages = {1326-1330},doi = {http://doi.ieeecomputersociety.org/10.1109/12.544491},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Fast Gossiping on Mesh-Bus ComputersIS - 11SN - 0018-9340SP1326EP1330EPD - 1326-1330A1 - Satoshi Fujita, A1 - Masafumi Yamashita, PY - 1996KW - Routing algorithmKW - mesh computerKW - shared busKW - gossipingKW - packet lengthKW - optimal time bound.VL - 45JA - IEEE Transactions on ComputersER -

Abstract—A mesh-bus computer is a parallel computer in which nodes (i.e., processors) are arranged on a two-dimensional array, and nodes on each row and nodes on each column, respectively, are connected by a shared bus. The nodes communicate with each other by exchanging packets through shared buses in CREW manner. Suppose that each node initially contains a piece of information called a token. A gossiping problem is the routing problem of exchanging tokens among all nodes in the computer, which has been studied extensively as a basic communication scheme for sharing information among nodes in a parallel computer. In this paper, we propose three gossiping algorithms for mesh-bus computers assuming that each packet can carry at most $\ell$ tokens in a step, where $\ell$ is a function of the number of all nodes. It is shown that by selecting the fastest algorithm among them, for each given function $\ell$, a lower bound on the gossiping time can be attained asymptotically.

[1] A. Bar-Noy and D. Peleg, "Square Meshes Are Not Always Optimal," IEEE Trans. Computers, vol. 40, pp. 196-204, 1991
[2] Y.C. Chen, W.T. Chen, G.H. Chen, and J.P. Sheu, "Designing Efficient Parallel Algorithms on Mesh Connected Computers with Multiple Broadcasting," IEEE Trans. Parallel and Distributed Systems, vol. 1, pp. 241-246, 1990.
[3] S. Cheung and F.C.M. Lau, "A Lower Bound for Permutation Routing on Two-Dimensional Bused Meshes," Information Processing Letters, vol. 45, pp. 225-228, Apr. 1993.
[4] S. Fujita and M. Yamashita, "Optimal Gossiping in Mesh-Bus Computers," Parallel Processing Letters, vol. 3, pp. 357-361, 1993.
[5] J.R. Goodman and P.J. Woest, “The Wisconsin Multicube: A New Large-Scale Cache-Coherent Multiprocessor,” Proc. 15th Ann. Int'l Symp. Computer Architecture, pp. 422-431, 1988.
[6] S.M. Hedetniemi, S.T. Hedetniemi, and A.L. Liestman, "A Survey of Gossiping and Broadcasting in Communication Networks," Networks, vol. 18, pp. 319-349, 1988.
[7] K. Iwama and Y. Kambayashi, "An O(log n) Parallel Connectivity Algorithm on the Mesh of Buses," Proc. IFIP 11th World Computer Congress, pp. 305-310, 1989.
[8] K. Iwama, E. Miyano, and Y. Kambayashi, "Routing Problems on the Mesh of Buses," Proc. ISAAC '92 (Lecture Notes in Computer Science 650). Springer-Verlag, 1992.
[9] D.W. Krumme, G. Cybenko, and K.N. Venkataraman, “Gossiping in Minimal Time,” SIAM J. Computing, vol. 21, no. 1, pp. 111-139, Feb. 1992.
[10] V.K. Prasanna Kumar and C.S. Raghavendra, "Array Processor with Multiple Broadcasting," Proc. 12th Int'l Symp. Computer Architecture, pp. 2-10, 1985.
[11] K. Nakano, T. Masuzawa, and N. Tokura, "Optimal Sorting Algorithms on Processor Arrays with Multiple Buses," Technical Report COMP, IEICE Japan, 91-7, 1991.
[12] Q.F. Stout, "Meshes with Multiple Buses," Proc. 27th FOCS, pp. 264-273, 1986.

Index Terms:
Routing algorithm, mesh computer, shared bus, gossiping, packet length, optimal time bound.
Citation:
Satoshi Fujita, Masafumi Yamashita, "Fast Gossiping on Mesh-Bus Computers," IEEE Transactions on Computers, vol. 45, no. 11, pp. 1326-1330, Nov. 1996, doi:10.1109/12.544491