Communication algorithms with advice

Pierre Fraigniaud (1) , David Ilcinkas (2, 3) , Andrzej Pelc (4)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 CEPAGE - Algorithmics for computationally intensive applications over wide scale distributed platforms
4 DII - Département d'Informatique et d'Ingénierie

We study the amount of knowledge about a communication network that must be given to its nodes in order to efficiently disseminate information. Our approach is {\em quantitative}: we investigate the minimum total number of bits of information (minimum size of advice) that has to be available to nodes, regardless of the type of information provided. We compare the size of advice needed to perform broadcast and wakeup (the latter is a broadcast in which nodes can transmit only after getting the source information), both using a linear number of messages (which is optimal). We show that the minimum size of advice permitting the {\em wakeup} with a linear number of messages in a $n$-node network, is $\Theta (n \log n)$, while the {\em broadcast} with a linear number of messages can be achieved with advice of size $O(n)$. We also show that the latter size of advice is almost optimal: no advice of size $o(n)$ can permit to broadcast with a linear number of messages. Thus an efficient wakeup requires strictly more information about the network than an efficient broadcast.

Keywords: Algorithm; Broadcasting; Wakeup; Size of advice; Message complexity; Network; Graph

Domains: Distributed, Parallel, and Cluster Computing [cs.DC]

Pierre Fraigniaud, David Ilcinkas, Andrzej Pelc. Communication algorithms with advice. Journal of Computer and System Sciences, 2010, 76 (3-4), pp.222-232. ⟨10.1016/j.jcss.2009.07.002⟩. ⟨hal-00412058⟩