Randomized generation of acyclic orientations upon anonymous distributed systems

  • Authors:

  • Gladstone M. Arantes, Jr.;Felipe M. G. França;Carlos A. Martinhon

  • Affiliations:

  • Universidade Federal do Rio de Janeiro, COPPE, Systems Engineering and Computer Science Program, Caixa Postal 68511, 21941-972, Rio de Janeiro, RJ, Brazil;Universidade Federal do Rio de Janeiro, COPPE, Systems Engineering and Computer Science Program, Caixa Postal 68511, 21941-972, Rio de Janeiro, RJ, Brazil;Universidade Federal Fluminense-UFF, Department of Computer Science, Institute of Computation, Rua Passo da Pátria 156, São Domingos, Niteroi, RJ, 24210-240, Brazil

  • Venue:
  • Journal of Parallel and Distributed Computing
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper presents two new randomized distributed algorithms for the generation of acyclic orientations upon anonymous distributed systems of arbitrary topology. Both algorithms, called Alg-Neighbors and Alg-Edges, make use of biased and unbiased dice having f=2 faces, and are analyzed in terms of correctness, expected time complexity and rate of convergence. First, the Alg-Neighbors algorithm is presented as a generalization of the Calabrese/Franca algorithm for dice (or coins) with 2 faces. It is proved that a convenient biasing function applied to all dice changes the expected time complexity from sub-exponential, i.e., O(f(ff-1)^n^-^1) (for unbiased dice with f faces), to O(n), where n is the number of the system's nodes. Next, it is shown that the Alg-Edges algorithm is able to produce acyclic orientations in O(log"fm) steps with high probability, where m denotes the total number of edges. Finally, a speed of convergence versus quality of acyclic orientation generation (associated number of colors) tradeoff is identified between Alg-Neighbors and Alg-Edges algorithms. Computational experiments were carried out in order to provide a more accurate description of the behavior of both algorithms.