ResumoEste artigo apresenta um novo algoritmo distribuído probabilístico para a geração de orientações acíclicas em um sistema distribuído anônimo de topologia arbitrária. O algoritmo é analisado tanto em termos de correção e complexidade esperada quanto velocidade de convergência. Em particular, é demonstrado que este novo algoritmo, chamado Alg-Arestas, é capaz de produzir, com alta probabilidade, orientações acíclicas quase instantaneamente, isto é, em menos de dois passos. Duas aplicações para essa forma de quebra de simetria serão discutidas: (i) inicialização do Escalonamento por Reversão de Arestas (ERA), um simples e poderoso algoritmo de escalonamento distribuído, e (ii) uma estratégia de distribuição de uploads em redes de computadores.Palavras-chave: algoritmos distribuídos probabilísticos; quebra de simetria; sistemas anônimos.
AbstractThis paper presents a new randomized distributed algorithm for the generation of acyclic orientations upon anonymous distributed systems of arbitrary topology. This algorithm is analyzed in terms of correctness and complexity as well as its convergence rate. In particular, it is shown that this new algorithm, called Alg-Arestas, is able to produce, with high probability, acyclic orientations quasi instantaneously, i.e., in less than two steps. Two applications of this form of symmetry breaking will be discussed: (i) initialization of Scheduling by Edge Reversal (SER), a simple and powerful distributed scheduling algorithm, and (ii) a strategy for distributed uploading in computer networks.
Scheduling by Edge Reversal provides an order of operation for nodes in a graph, but maximizing or minimizing the resulting concurrency is hard. In this paper, we discuss a series of real‐world applications for this technique and propose algorithms for both problems. For maximum concurrency, we prove its general inapproximability and introduce approximation algorithms for classes of graphs. For minimum concurrency, we use hardness and inapproximability results to establish its relation to longest cycles, while also introducing a novel application for assembling musical phrases.
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