Sobre processos de aglomeração distribuída

Abstract

In a distributed clustering algorithm introduced by Coffman, Courtois,Gilbert and Piret [5], each vertex of Z^d receives an initial amount of resource, at each iteration, transfers all of its resource to the neighboring vertex which currently holds the maximum amount of resource. It proves in this work that for a initial distribution of resources invariant under lattice translations, the flow of resource at each vertex terminates after finitely many steps and that resources nevertheless escape to infinity, in sense that the final amount of resource at a given vertex is strictly smaller in expectation than the initial amount.