Gossiping in vertex-disjoint paths mode in d-dimensional grids and planar graphs
Effective one-way and two-way gossip algorithms for d-dimensional grids, d≥2, are designed.
The lower bound 2 log2n −log2k −log2 log2n −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.
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”).
KeywordsPlanar Graph Complete Graph Interconnection Network Communication Mode Outerplanar Graph
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