On the Computational Power of Simple Dynamics

Sur la puissance de calcul de le dynamiques simples

Emanuele Natale (1)

1 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]

This work presents a set of analytical results regarding some elementary randomized protocols, called \emph{dynamics}, for solving some fundamental computational problems. New techniques for analyzing the processes that arise from such dynamics are presented, together with concrete examples on how to build efficient and robust distributed algorithms for some important tasks using these processes as a black-box. More specifically, we analyze several dynamics such as the 3-Majority, the Averaging and the Undecided-State ones, and we show how to use them to solve fundamental problems such as plurality consensus, community detection (including the reconstruction problem in the stochastic block model), and bit dissemination (rumor spreading). We focus mainly on unstructured and random interaction models, and we also deal with scenarios in which the communication is affected by noise or when a self-stabilizing protocol is required.

Ce travail présente un ensemble de résultats d'analyse portant sur certains élémentaires protocoles randomisés, appelés \emph{dynamics}, pour résoudre certains problèmes fondamentaux de calcul. De nouvelles techniques d'analyse de ces dynamiques sont présentées, accompagnées d'exemples concrets sur comment construire des algorithmes distribués efficaces et robustes pour certains des tâches importantes en utilisant ces processus comme une black-box.

Mots clés: Distributed computing

Mots clés: Calcul distribué

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Emanuele Natale. On the Computational Power of Simple Dynamics. Distributed, Parallel, and Cluster Computing [cs.DC]. Sapienza University of Rome, 2017. English. ⟨NNT : ⟩. ⟨tel-02002681⟩