Abstract
We study the multiparty communication model where players are the nodes of a network and each of these players knows his/her own identifier together with the identifiers of his/her neighbors. The players simultaneously send a unique message to a referee who must decide a graph property. The goal of this article is to separate, from the point of view of message size complexity, three different settings: deterministic protocols, randomized protocols with private coins and randomized protocols with public coins. For this purpose we introduce the boolean function Twins. This boolean function returns 1 if and only if there are two nodes with the same neighborhood.
This work has been partially supported by CONICYT via Basal in Applied Mathematics (I.R.), Núcleo Milenio Información y Coordinación en Redes ICM/FI P10-024F (I.R.) and Fondecyt 1130061 (I.R.)
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Becker, F., Montealegre, P., Rapaport, I., Todinca, I. (2014). The Simultaneous Number-in-Hand Communication Model for Networks: Private Coins, Public Coins and Determinism. In: Halldórsson, M.M. (eds) Structural Information and Communication Complexity. SIROCCO 2014. Lecture Notes in Computer Science, vol 8576. Springer, Cham. https://doi.org/10.1007/978-3-319-09620-9_8
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DOI: https://doi.org/10.1007/978-3-319-09620-9_8
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