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Tight Bounds for Broadcasting in the Linear Cost Model

Bruno Beauquier 1 Olivier Delmas Stéphane Pérennes
1 SLOOP - Simulation, Object Oriented Languages and Parallelism
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
Abstract : 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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Submitted on : Wednesday, May 24, 2006 - 11:03:49 AM
Last modification on : Friday, February 4, 2022 - 3:20:18 AM
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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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