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Master's Dissertation
DOI
10.11606/D.100.2018.tde-06092018-144335
Document
Author
Full name
Fábio Tosetto Reale
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2018
Supervisor
Committee
Mendonca, Jose Ricardo Goncalves de (President)
Coletti, Cristian Favio
Hase, Masayuki Oka
Lima, Karla Roberta Pereira Sampaio
Title in Portuguese
Métodos de Monte Carlo para amostragem de permutações com restrições e aplicações
Keywords in Portuguese
Amostragem sequencial por importância
Matrizes aleatórias 0-1
Permanente
Permutação com restrições
Processo de exclusão
Abstract in Portuguese
Neste trabalho definimos o processo de exclusão simples simétrico em tempo discreto sobre grafos por meio de permutações com restrições sobre os índices dos vértices dos grafos. O processo é uma generalização das permutações dos índices do grafo completo. Apresentamos algoritmos de Monte Carlo e de amostragem sequencial por importância para amostrar permutações com restrições inspirados pelo problema análogo de calcular permanentes. Como aplicação, utilizamos esses algoritmos para estimar os tempos de relaxação do processo de exclusão simples simétrico em tempo discreto sobre grafos aleatórios densos de Erdös-Rényi com laços
Title in English
Monte Carlo sampling of restricted permutations and aplications
Keywords in English
Exclusion process
Permanent
Random 0-1 matrix
Restricted permutation
Sequential importance sampling
Abstract in English
In this work we define the symmetric simple exclusion process in discrete time over graphs by means of suitably restricted permutations over the labels of the vertices of the graphs. The process is a generalization of the shuffling of labels on the complete graph. Straightforward Monte Carlo and sequential importance sampling algorithms to sample restricted permutations inspired by the related problem of computing permanents are discussed. We illustrate the formalism by estimating the relaxation times of the symmetric simple exclusion process in discrete time over dense loop-augmented Erdös-Rényi random graphs
 
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Publishing Date
2018-09-13
 
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