scholarly journals Improved Bounds for Perfect Sampling of $k$-Colorings in Graphs

2022 ◽  
pp. STOC20-54-STOC20-74
Author(s):  
Siddharth Bhandari ◽  
Sayantan Chakraborty
Keyword(s):  
Perfect Sampling

scholarly journals Perfect sampling for infinite server and loss systems

2015 ◽  
Vol 47 (03) ◽  
pp. 761-786 ◽  
Author(s):  
Jose Blanchet ◽  
Jing Dong
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Heavy Traffic ◽  
Arrival Rate ◽  
Marked Point Processes ◽  
Perfect Sampling ◽  
Running Time ◽  
Infinite Server ◽  
Loss Systems ◽  
Server System

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.

PERFECT STOCHASTIC SUMMATION IN HIGH ORDER FEYNMAN GRAPH EXPANSIONS

2006 ◽  
Vol 17 (11) ◽  
pp. 1527-1549 ◽  
Author(s):  
J. N. CORCORAN ◽  
U. SCHNEIDER ◽  
H.-B. SCHÜTTLER
Keyword(s):  
Monte Carlo ◽  
Feynman Graph ◽  
Sampling Technique ◽  
Small Samples ◽  
Brute Force ◽  
Perfect Sampling ◽  
Self Energy ◽  
Graph Expansions ◽  
Low Dimensional ◽  
True Values

We describe a new application of an existing perfect sampling technique of Corcoran and Tweedie to estimate the self energy of an interacting Fermion model via Monte Carlo summation. Simulations suggest that the algorithm in this context converges extremely rapidly and results compare favorably to true values obtained by brute force computations for low dimensional toy problems. A variant of the perfect sampling scheme which improves the accuracy of the Monte Carlo sum for small samples is also given.

The Move-to-Front Rule: A Case Study for two Perfect Sampling Algorithms

1998 ◽  
Vol 12 (3) ◽  
pp. 283-302 ◽  
Author(s):  
James Allen Fill
Keyword(s):  
Finite Population ◽  
Mixing Time ◽  
Test Case ◽  
Perfect Sampling ◽  
Mcmc Algorithms ◽  
Time Result ◽  
Elementary Problem ◽  
Sampling Algorithms ◽  
Coupling Algorithm

The elementary problem of exhaustively sampling a finite population without replacement is used as a nonreversible test case for comparing two recently proposed MCMC algorithms for perfect sampling, one based on backward coupling and the other on strong stationary duality. The backward coupling algorithm runs faster in this case, but the duality-based algorithm is unbiased for user impatience. An interesting by-product of the analysis is a new and simple stochastic interpretation of a mixing-time result for the move-to-front rule.

scholarly journals Perfect sampling using bounding chains

2004 ◽  
Vol 14 (2) ◽  
pp. 734-753 ◽  
Author(s):  
Mark Huber
Keyword(s):  
Perfect Sampling

scholarly journals Perfect and nearly perfect sampling of work-conserving queues

2015 ◽  
Vol 80 (3) ◽  
pp. 197-222 ◽  
Author(s):  
Yaofei Xiong ◽  
Duncan J. Murdoch ◽  
David A. Stanford
Keyword(s):  
Perfect Sampling
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