Abstract
The communication modes (one-way and two-way mode) used for disseminating information among 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). Since optimal broadcast and accumulation algorithms for these modes can be achieved in a straightforward way for almost all interconnection networks used, the paper concentrates on the gossip problem. The main results are listed below:
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1.
Optimal gossip algorithms for paths, complete graphs and flakes in both modes.
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2.
For hypercubes, cube-connected cycles, butterfly networks, etc., gossip algorithms which are only about O(log2 log2 n) rounds slower than the optimal gossip algorithms on complete graphs are designed. Furthermore, it is shown that at least Ω(log2 log2 log2 n) rounds more than needed by the optimal gossip algorithm on the complete graph are necessary for every “well-structured” gossip algorithm on networks with “small” degree.
Note that the results achieved have also practical application, because the vertex-disjoint paths mode can be implemented in several hardware realisations of computing networks.
This work was partially supported by 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.
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© 1994 Springer-Verlag Berlin Heidelberg
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Hromkovič, J., Klasing, R., Stöhr, E.A. (1994). Gossiping in vertex-disjoint paths mode in interconnection networks. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1993. Lecture Notes in Computer Science, vol 790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57899-4_60
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DOI: https://doi.org/10.1007/3-540-57899-4_60
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