Skip to Main content Skip to Navigation

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.
Document type :
Complete list of metadata

Cited literature [1 references]  Display  Hide  Download
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 11:03:49 AM
Last modification on : Wednesday, October 14, 2020 - 4:24:17 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:24:08 PM


  • 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⟩



Record views


Files downloads