Optimal algorithms for dissemination of information in generalized communication modes
Some generalized communication modes enabling the dissemination of information among processors of interconnection networks via vertex-disjoint or edge-disjoint paths in one communication step are investigated. A thorough study of these communication modes is presented by giving optimal algorithms for broadcasting, accumulation and gossiping in most of the well known parallel architectures. For those networks in which a hamiltonian path exists (hypercubes, cube connected cycles, butterflies, etc.), optimal algorithms are obtained quite easily. But for complete binary trees, complete k-ary trees (k≥3) and arbitrary k-degree bounded graphs, the optimal algorithms as well as the matching lower bound proofs are more involved. An interesting consequence of the presented algorithms is the fact that in almost all these interconnection networks the gossip problem cannot be solved in time less than the sum of time complexities of the accumulation problem and the broadcast problem (i.e. for most networks the optimal algorithm for the gossip problem is simply the concatenation of optimal algorithms for accumulation and broadcasting).
KeywordsOptimal Algorithm Interconnection Network Information Dissemination Communication Mode Hamiltonian Path
Unable to display preview. Download preview PDF.
- [ALMN90]B. Aiello, T. Leighton, B. Maggs, and M. Newman. Fast algorithms for bit-serial routing on a hypercube. 2nd ACM Symposium on Parallel Algorithms and Architectures, pages pp. 55–64, 1990.Google Scholar
- [BAPRS90]Y. Ben-Asher, D. Peleg, R. Ramaswami, and A. Schuster. The power of reconfiguration. Technical report, The Hebrew University, Jerusalem, 1990.Google Scholar
- [BHMS90]A. Bagchi, S. L. Hakimi, J. Mitchem, and E. Schmeichel. Parallel algorithms for gossiping by mail. Inf. Proc. Letters, (34):pp 197–202, 1990.Google Scholar
- [BS72]B. Baker and R. Shostak. Gossips and telephones. Diser. Mathem., (2):pp 191–193, 1972.Google Scholar
- [DS87]W. Dally and C. Seitz. Deadlock free message routing in multiprocessor interconnection networks. IEEE Transactions on Computers, C-36(5), pages pp 547–553, 1987.Google Scholar
- [EM89]S. Even and B. Monien. On the number of rounds necessary to disseminate information. In: Proc. 1st ACM Symp. on Parallel Algorithms and Architectures, pages pp 318–327, 1989.Google Scholar
- [Far80]A.M. Farley. Minimum-time line broadcast networks. Networks, (10):pp 59–70, 1980.Google Scholar
- [HHL88]S.M. Hedetniemi, S.T. Hedetniemi, and A.L. Liestman. A survey of gossiping and broadcasting in communication networks. Networks, (18):pp 319–349, 1988.Google Scholar
- [HJM90]J. Hromkovic, C.D. Jeschke, and B. Monien. Optimal algorithms for dissemination of information in some interconnection networks. In: Proc. of 15th MFCS'90, LNCS 452 (1990), pages pp 337–346, 1990.Google Scholar
- [HMS72]A. Hajnal, E.C. Milner, and E. Szemeredi. A cure for the telephone disease. Can. Math. Bull., (15):pp 447–450, 1972.Google Scholar