## Optimal Sequential Gossiping by Short Messages (1998)

Venue: | DAMATH: DISCRETE APPLIED MATHEMATICS AND COMBINATORIAL OPERATIONS RESEARCH AND COMPUTER SCIENCE, VOL 86 |

Citations: | 14 - 4 self |

### BibTeX

@INPROCEEDINGS{Bermond98optimalsequential,

author = {Jean-Claude Bermond and Luisa Gargano and Stephane Perennes},

title = {Optimal Sequential Gossiping by Short Messages},

booktitle = {DAMATH: DISCRETE APPLIED MATHEMATICS AND COMBINATORIAL OPERATIONS RESEARCH AND COMPUTER SCIENCE, VOL 86},

year = {1998},

pages = {145--155},

publisher = {}

}

### OpenURL

### Abstract

Gossiping is the process of information diffusion in which each node of a network holds a block that must be communicated to all the other nodes in the network. We consider the problem of gossiping in communication networks under the restriction that communicating nodes can exchange up to a fixed number p of blocks during each call. We study the minimum numbers of call necessary to perform gossiping among n processor for any arbitrary fixed upper bound on the message size p.

### Citations

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(Show Context)
Citation Context ...the knowledge of each node after the first phase. Thesindicates the nodes of type k. 0 [0,1] 1 [0,2] 2 [0,3] 3 [0,4] 4 [0,5] 5 [0,6] 6 [0,7] 7 [0,8] 8 [0,11] 9 [0,9] 10 [1,10] 11* [2,14] 12 [3,12] 13 =-=[4,13]-=- 14* [5,17] 15 [6,15] 16 [7,16] 17* [8,20] 18 [9,18] 19 [10,19] 20 [11,21] 21 [12,21] The following table gives the interval of blocks known by each node after the second phase before and after the re... |

105 | E.: Methods and problems of communication in usual networks
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(Show Context)
Citation Context ...6, 8, 16]. Due to the considerable practical relevance in parallel and distributed computation and the related interesting theoretical issues, gossiping has been extensively studied in the literature =-=[9, 13, 15]-=-. The great majority of the previous work on gossiping has considered the case in which the items of information known to a processor at any given time during the execution of the gossiping protocol c... |

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Citation Context ... node after the first phase. Thesindicates the nodes of type k. 0 [0,1] 1 [0,2] 2 [0,3] 3 [0,4] 4 [0,5] 5 [0,6] 6 [0,7] 7 [0,8] 8 [0,11] 9 [0,9] 10 [1,10] 11* [2,14] 12 [3,12] 13 [4,13] 14* [5,17] 15 =-=[6,15]-=- 16 [7,16] 17* [8,20] 18 [9,18] 19 [10,19] 20 [11,21] 21 [12,21] The following table gives the interval of blocks known by each node after the second phase before and after the relabeling, respectivel... |

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Citation Context ... in a large class of parallel computation problems, such as linear system solving, matrix manipulation, and sorting, where both input and output data are required to be distributed across the network =-=[6, 8, 16]-=-. Due to the considerable practical relevance in parallel and distributed computation and the related interesting theoretical issues, gossiping has been extensively studied in the literature [9, 13, 1... |

36 | R.L.Graham. Routing permutations on graphs via matching
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Citation Context ...l, has been considered in [4] and [3], respectively; analogous problems have been studied in [11, 10, 14, 12, 7, 5]. Packet routing in interconnection networks in the F 1 model has been considered in =-=[1]-=-. In this paper we give a lower bound on the minimum possible number of calls c(n; p) necessary to complete gossiping among n nodes under the condition that during each call communicating nodes can ex... |

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Citation Context ...mple 3.2 Let us consider p = 9 and n = 22; this implies k = 4. The following table gives the knowledge of each node after the first phase. Thesindicates the nodes of type k. 0 [0,1] 1 [0,2] 2 [0,3] 3 =-=[0,4]-=- 4 [0,5] 5 [0,6] 6 [0,7] 7 [0,8] 8 [0,11] 9 [0,9] 10 [1,10] 11* [2,14] 12 [3,12] 13 [4,13] 14* [5,17] 15 [6,15] 16 [7,16] 17* [8,20] 18 [9,18] 19 [10,19] 20 [11,21] 21 [12,21] The following table give... |

14 |
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Citation Context ...llowing table gives the knowledge of each node after the first phase. Thesindicates the nodes of type k. 0 [0,1] 1 [0,2] 2 [0,3] 3 [0,4] 4 [0,5] 5 [0,6] 6 [0,7] 7 [0,8] 8 [0,11] 9 [0,9] 10 [1,10] 11* =-=[2,14]-=- 12 [3,12] 13 [4,13] 14* [5,17] 15 [6,15] 16 [7,16] 17* [8,20] 18 [9,18] 19 [10,19] 20 [11,21] 21 [12,21] The following table gives the interval of blocks known by each node after the second phase bef... |

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Citation Context ...problem of minimizing the time (number of rounds) to complete the gossiping process in the H 1 and F 1 model, has been considered in [4] and [3], respectively; analogous problems have been studied in =-=[11, 10, 14, 12, 7, 5]-=-. Packet routing in interconnection networks in the F 1 model has been considered in [1]. In this paper we give a lower bound on the minimum possible number of calls c(n; p) necessary to complete goss... |

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7 |
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(Show Context)
Citation Context ...and 17, 8 and 20, 14 and 21. Relabelling the nodes of type 1 with labels from 0 to 13, we can organize calls among them so that we have 0 [13,0][1,9][4,12] 1 [14,1][2,10][5,13] 2 [16,3][4,12][7,15] 3 =-=[17,4]-=-[5,13][6,16] 4 [19,6][7,15][10,18] 5 [20,7][8,16][11,19] 6 [0,9][10,18][13,21] 7 [1,10][11,19][0,14] 8 [3,12][13,21][16,2] 9 [4,13][14,0][17,3] 10 [6,15][16,2][19,5] 11 [7,16][17,3][20,6] 12 [9,18][19... |

5 |
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Citation Context ...,11][15,2] 8 [4,8][9,12][0,3] 9* [5,12][1,4][13,0] 10 [6,10][11,14][2,5] 11 [7,11][12,15][3,6] 12* [8,15][4,7][0,3] 13 [9,13][14,1][5,8] 14 [10,14][15,2][6,9] 15* [11,2][7,10][3,6] = 0* ALL 1 [9,5] 2 =-=[10,6]-=- 3* ALL 4 [12,8] 5 [13,9] 6* ALL 7 [15,11] 8 [0,12] 9* ALL 10 [2,14] 11 [3,15] 12* ALL 13 [5,1] 14 [6,2] 15* ALL In the last phase the calls that complete the protocol are between nodes 1 and 8, 2 and... |

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Citation Context ...problem of minimizing the time (number of rounds) to complete the gossiping process in the H 1 and F 1 model, has been considered in [4] and [3], respectively; analogous problems have been studied in =-=[11, 10, 14, 12, 7, 5]-=-. Packet routing in interconnection networks in the F 1 model has been considered in [1]. In this paper we give a lower bound on the minimum possible number of calls c(n; p) necessary to complete goss... |

2 |
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Citation Context ...problem of minimizing the time (number of rounds) to complete the gossiping process in the H 1 and F 1 model, has been considered in [4] and [3], respectively; analogous problems have been studied in =-=[11, 10, 14, 12, 7, 5]-=-. Packet routing in interconnection networks in the F 1 model has been considered in [1]. In this paper we give a lower bound on the minimum possible number of calls c(n; p) necessary to complete goss... |

1 |
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