A Bridge Between the Asynchronous Message Passing Model and Local Computations in Graphs

Election in the Qualitative World

“…Using known results in distributed computing [6,9,13], we can show that in the anonymous setting, i.e., when the agents can understand each other but do not have distinct labels, there exists an election algorithm for an environment (G, E, p) if and only if the labelled digraph G = (Dir(G), χ p ) is symmetriccovering-minimal. Moreover, from Proposition 1, we know that if the symmetric digraph G = (Dir(G), χ p ) admits a non-trivial well-balanced automorphism σ, then G is a symmetric covering of G /Γ σ that is not isomorphic to G .…”

“…There exists a large variety of results for these problems in the mobile agent setting assuming different properties of the environment [2,4,5,10,11]. The election problem has also been extensively studied in the distributed setting, and particularly in anonymous networks, where the processes do not have distinct labels [1,6,9,13].…”

“…This implies that an election algorithm in the distributed mobile environment (G, E, p) must not use some particularity of the ports-labelling or make any assumption on the set of colors (for example, if one know that there is always a red agent, one can design an algorithm that elects the red agent). Note that, as for anonymous networks in the distributed setting [9,13], the protocols must not depend on the ports-labelling. Indeed, the role of the ports-labelling is just to enable an agent to make a distinction between the different neighbours of a vertex.…”

Modélisation algébrique du dîner des philosophes

“…Cette approche de la modélisation de calculs distribués, tout en offrant une approche différente, plus algébrique, n'est pas sans rappeler la modélisation par système de réécritures locales [6].…”

Model Driven capabilities of the DA-GRS model

“…A computation step is defined by a pair (pre-state, post-state), which makes it possible to focus on a general solution for a given problem. The way a GRS based algorithm can be adapted to a specific communication model (and especially to the asynchronous message passing model) has been discussed many times, see for instance [3] or [4] for more information.…”