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Reports Year : 1999

Tight Bounds for Broadcasting in the Linear Cost Model

Olivier Delmas
Stéphane Pérennes
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This work considers broadcast protocols made of successive communication rounds in the linear cost model: the time needed to send a message of length L is defined as \alpha +L\tau. In this model, the communication time of any algorithm \mathcal{A} is expressed as the sum R_\mathcalA\cdot\alp- ha +T_\mathcal{A} \cdot\tau, where R_\mathcalA is the number of rounds and T_\mathcalA the transmission cost of the algorithm. In order to design an efficient algorithm realizing a given communication pattern, it appears that minimizing R_\mathcalA and T_\mathcalA are antinomic goals. We study this trade-off issue for broadcast protocols. Surprisingly, such a general theoretical study has almost never been done. In the literature, only the two opposite issues are actually considered: minimizing the number of rounds in the case of short messages, or minimizing the transmission cost in the case of large messages. Our results concern the fully-connected N-nodes network K_N, with N=(k+1)^T, in the bidirectional k-ports mode. We derive tight bounds on the communication time for broadcasting in T+r rounds, our lower bounds holding for any network.


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Dates and versions

inria-00072831 , version 1 (24-05-2006)


  • HAL Id : inria-00072831 , version 1


Bruno Beauquier, Olivier Delmas, Stéphane Pérennes. Tight Bounds for Broadcasting in the Linear Cost Model. RR-3827, INRIA. 1999. ⟨inria-00072831⟩
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