Algorithms in Monte Carlo Methods

Dear Colleagues,

Monte Carlo methods, in the most general sense, encompass algorithms that can be characterized by two key features: (1) they use random choices in their operation; and (2) they relax the requirement of insisting on a deterministically correct result. A Monte Carlo method may produce a solution that is correct only with high probability (but not with certainty), with respect to the internal random choices of the algorithm.

Such an algorithm can have a variety of goals. It may solve a deterministic problem, for example, finding a minimum cut in a graph. It may look for an approximate solution of a numerical task, including optimization and numerical integration. The target can also be inherently random, such as drawing a random sample from a complicated probability distribution.

The key issue in designing a Monte Carlo method is to find an algorithm that can capitalize on the random choices to efficiently produce a result, which is correct with high probability. In some cases, such an algorithm is completely problem specific; examples include the Karger–Stein minimum cut algorithm and various randomized primality tests. However, there are useful general schemes which provide solutions to a multitude of tasks. Quite a few such schemes exist. These include general-purpose randomized optimization methods such as simulated annealing, genetic algorithm, solutions for optimal stopping, change-point detection, the Moser–Tardos algorithm, etc. Another class of methods aim at producing random samples from complex probability distributions, including rejection sampling, importance sampling, the cross-entropy method, Markov chain Monte Carlo algorithms, and others.

This is a broad and rich research area. Topics of interest include, but are not limited to, the following:

• Randomized algorithms for graph problems and combinatorial optimization;
• Randomized algorithms for continuous optimization;
• Randomized algorithms for numerical problems;
• Methods for generating random samples from complex probability distributions;
• Optimal stopping rules;
• Change-point detection methods;
• Markov chain Monte Carlo algorithms;
• Estimation of mixing rate in Markov chains;
• Computational complexity issues relating to Monte Carlo methods;
• Case studies of solving practical problems via Monte Carlo methods.

Dr. Georgy Sofronov
Prof. Dr. Andras Farago
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.