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Speeding up the FMMR perfect sampling algorithm: A case study revisited
Author(s) -
Dobrow Robert P.,
Fill James Allen
Publication year - 2003
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.10096
Subject(s) - markov chain , speedup , markov chain monte carlo , sampling (signal processing) , computer science , algorithm , monotonic function , state (computer science) , running time , rejection sampling , exploit , exponential function , mathematics , monte carlo method , mathematical optimization , hybrid monte carlo , statistics , parallel computing , mathematical analysis , computer security , filter (signal processing) , machine learning , computer vision
Abstract In a previous paper by the second author, two Markov chain Monte Carlo perfect sampling algorithms—one called coupling from the past (CFTP) and the other (FMMR) based on rejection sampling—are compared using as a case study the move‐to‐front (MTF) self‐organizing list chain. Here we revisit that case study and, in particular, exploit the dependence of FMMR on the user‐chosen initial state. We give a stochastic monotonicity result for the running time of FMMR applied to MTF and thus identify the initial state that gives the stochastically smallest running time; by contrast, the initial state used in the previous study gives the stochastically largest running time. By changing from worst choice to best choice of initial state we achieve remarkable speedup of FMMR for MTF; for example, we reduce the running time (as measured in Markov chain steps) from exponential in the length n of the list nearly down to n when the items in the list are requested according to a geometric distribution. For this same example, the running time for CFTP grows exponentially in n . © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003