Abstract
The communication modes (one-way and two-way mode) used for sending messages to processors of interconnection networks via vertex-disjoint paths in one communication step are investigated. The complexity of communication algorithms is measured by the number of communication steps (rounds). Here, the complexity of gossiping in grids and in planar graphs is investigated. The main results are the following:
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1.
Effective one-way and two-way gossip algorithms for d-dimensional grids, d≥2, are designed.
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2.
The lower bound 2 log2 n −log2 k −log2 log2 n −2 is established on the number of rounds of every two-way gossip algorithm working on any graph of n nodes and vertex bisection k. This proves that the designed two-way gossip algorithms on d-dimensional grids, d≥3, are almost optimal, and it also shows that the 2-dimensional grid belongs to the best gossip graphs among all planar graphs.
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3.
Another lower bound proof is developed to get some tight lower bounds on one-way “well-structured” gossip algorithms on planar graphs (note that all gossip algorithms designed until now in vertexdisjoint paths mode are “well-structured”).
This work was partially supported by grants Mo 285/4-1, Mo 285/9-1 and Me 872/6-1 (Leibniz Award) of the German Research Association (DFG), and by the ESPRIT Basic Research Action No. 7141 (ALCOM II).
This author was partially supported by SAV Grant No. 88 and by EC Cooperation Action IC 1000 Algorithms for Future Technologies.
This author was supported by the Ministerium für Wissenschaft und Forschung des Landes Nordrhein-Westfalen.
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References
Y. Ben-Asher, D. Peleg, R. Ramaswami, A. Schuster, ”The power of reconfiguration”, Technical Report, The Hebrew University, Jerusalem, 1990.
K. Diks, H.N. Djidjev, O. Sykora, I. Vrto, ”Edge separators of planar and outerplanar graphs with applications”, Journal of Algorithms 14 (1993), pp. 258–279.
W. Dally, C. Seitz, ”Deadlock free message routing in multiprocessor interconnection networks”, IEEE Transactions on Computers 36 (1987), pp. 547–553.
S. Even, B. Monien, “On the number of rounds necessary to disseminate information”, Proc. 1st ACM Symp. on Parallel Algorithms and Architectures (SPAA'89), 1989, pp. 318–327.
A.M. Farley, “Minimum-Time Line Broadcast Networks”, Networks 10 (1980), pp. 59–70.
R. Feldmann, J. Hromkovič, S. Madhavapeddy, B. Monien, P. Mysliwietz, “Optimal algorithms for dissemination of information in generalized communication modes”, Proc. Parallel Architectures and Languages Europe (PARLE'92), Lecture Notes in Computer Science 605, Springer Verlag 1992, pp. 115–130.
J. Hromkovič, R. Klasing, E.A. Stöhr, ”Gossiping in vertex-disjoint paths mode in interconnection networks”, Proc. 19th Int. Workshop on Graph-Theoretic Concepts in Computer Science (WG '93), Lecture Notes in Computer Science, Springer Verlag 1993, to appear.
M. Klawe, F.T. Leighton, ”A tight lower bound on the size of planar permutation networks”, SIAM J. Disc. Math. 5 (1992), No. 4, pp. 558–563.
R.J. Lipton, R.E. Tarjan, ”A separator theorem for planar graphs”, SIAM J. Appl. Math. 36 (1979), No. 2, pp. 177–189.
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© 1993 Springer-Verlag Berlin Heidelberg
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Hromkovič, J., Klasing, R., Stöhr, E.A., Wagener, H. (1993). Gossiping in vertex-disjoint paths mode in d-dimensional grids and planar graphs. In: Lengauer, T. (eds) Algorithms—ESA '93. ESA 1993. Lecture Notes in Computer Science, vol 726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57273-2_56
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DOI: https://doi.org/10.1007/3-540-57273-2_56
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