## Gossiping in Vertex-Disjoint Paths Mode in d-Dimensional Grids and Planar Graphs (Extended Abstract) (1993)

Venue: | Information and Computation |

Citations: | 8 - 2 self |

### BibTeX

@INPROCEEDINGS{Hromkovic93gossipingin,

author = {Juraj Hromkovic and Ralf Klasing and Elena A. Stohr and Hubert Wagener},

title = {Gossiping in Vertex-Disjoint Paths Mode in d-Dimensional Grids and Planar Graphs (Extended Abstract)},

booktitle = {Information and Computation},

year = {1993},

pages = {200--211},

publisher = {Springer Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

Juraj Hromkovic y , Ralf Klasing, Elena A. Stohr, Hubert Wagener z Department of Mathematics and Computer Science University of Paderborn, 33095 Paderborn, Germany 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: 1. Effective one-way and two-way gossip algorithms for d-dimensional grids, d 2, are designed. 2. The lower bound 2 log 2 n \Gamma log 2 k \Gamma log 2 log 2 n \Gamma 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 al...

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Citation Context ...\Delta blog 2 nc + 7. Proof. The proof is analogous to the one of the previous theorem. Only the search for vertex-disjoint paths implementing the optimal one-way gossip algorithm for complete graphs =-=[EM89]-=- is a little more complicated (see Fig. 1 for the implementation of a round of the algorithm given in [EM89], the notation in Fig. 1 is according to [EM89]). The only change in the complexity of the a... |

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Citation Context ...one round in graphs having a Hamiltonian path) that the designed algorithms met the trivial lower bounds. The one-way vertex-disjoint paths mode introduced (but not thoroughly investigated) by Farley =-=[Fa80]-=- is not as powerful as the LDVP mode, and so proving the effectivity of designed algorithms requires to develop new, special lower bound techniques. The 1VPD/2VDP mode has been investigated in [HKS93]... |

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Citation Context ... n \Gamma \Theta(log 2 log 2 n) for any constant ds3. Lipton and Tarjan [LT79] gave an upper bound of p 8 \Delta n on the vertex bisection of any planar graph P l n of n nodes (consider the result in =-=[DDSV93]-=- to see why we use vertex bisection instead of edge bisection in the proof of Lemma 4.1). Applying Lemma 4.1 and recalling Theorem 3.1, we obtain the result that the 2-dimensional square grid Gr 2 n i... |

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Citation Context ...her vertices in P . Thus, after the execution of the round all vertices of each path P know the message submitted from the sending endpoint. The listen-in vertex-disjoint paths mode was introduced in =-=[FHMMM92]-=-, where optimal (or almost optimal) broadcast, accumulation, and gossip algorithms for almost all basic interconnection networks were found. This was possible mostly because the LVDP mode is so powerf... |

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(Show Context)
Citation Context ... [Fa80] is not as powerful as the LDVP mode, and so proving the effectivity of designed algorithms requires to develop new, special lower bound techniques. The 1VPD/2VDP mode has been investigated in =-=[HKS93]-=-, where optimal algorithms for paths (approximately 2 log 2 n rounds in both VDP modes), complete graphs (log 2 n rounds in 2VDP mode and 1:44::: log 2 n rounds in 1VDP mode), and flakes are designed,... |

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