Simulated division with approximate factoring for the multiple recursive generator with both unrestricted multiplier and non-mersenne prime modulus

AbstractThis paper focuses on devising a general and efficient way of generating random numbers for the multiple recursive generator with both unrestricted multiplier and non-Mersenne prime modulus. We propose a new algorithm that embeds the technique of approximate factoring into the simulated division method. The proposed new algorithm improves the decomposition method in terms of both the suitability for various word-sizes of the computers and the efficiency characteristics, such as the number of arithmetic operations required and the computational time. Empirical simulations are conducted to compare and evaluate the computational time of this algorithm with the decomposition method for various computers

Generation of cubic graphs

We describe a new algorithm for the efficient generation of all non-isomorphic connected cubic graphs. Our implementation of this algorithm is more than 4 times faster than previous generators. The generation can also be efficiently restricted to cubic graphs with girth at least 4 or 5

Design, Search and Implementation of Improved Large Order Multiple Recursive Generators and Matrix Congruential Generators

Large order, maximum period multiple recursive generators (MRGs) with few nonzero terms (e.g., DX-k-s generators) have become popular in the area of computer simulation. They are efficient, portable, have a long period, and have the nice property of high-dimensional equi-distribution. The latter two properties become more advantageous as k increases. The performance on the spectral test, a theoretical test that provides some measure of uniformity in dimensions beyond the MRG\u27s order k, could be improved by choosing multipliers that yield a better spectral test value. We propose a new method to compute the spectral test which is simple, intuitive, and efficient for some special classes of large order MRGs. Using this procedure, we list \u27\u27better\u27\u27 FMRG-k and DX-k-s generators with respect to performance on the spectral test. Even so, MRGs with few nonzero terms do not perform as well with respect to the spectral test as MRGs with many nonzero terms. However, MRGs with many nonzero terms can be inefficient or lack a feasible parallelization method, i.e., a method of producing substreams of (pseudo) random numbers that appear independent. To implement these MRGs efficiently and in parallel, we can use an equivalent recursion from another type of generator, the matrix congruential generator (MCG), a k-dimensional generalization of a first order linear recursion where the multipliers are embedded in a k by k matrix. When MRGs are used to construct MCGs and the recursion of the MCG is implemented k at a time for a k-dimensional vector sequence, then the MCG mimics k copies of a MRG in parallel with different starting seeds. Therefore, we propose a method for efficiently finding MRGs with many nonzero terms from an MRG with few nonzero terms and then give an efficient and parallel MCG implementation of these MRGs with many nonzero terms. This method works best for moderate order k. For large order MRGs with many nonzero terms, we propose a special class called DW-k. This special class has a characteristic polynomial that yields many nonzero terms and corresponds to an efficient and parallel MCG implementation

Online Causal Structure Learning in the Presence of Latent Variables

We present two online causal structure learning algorithms which can track changes in a causal structure and process data in a dynamic real-time manner. Standard causal structure learning algorithms assume that causal structure does not change during the data collection process, but in real-world scenarios, it does often change. Therefore, it is inappropriate to handle such changes with existing batch-learning approaches, and instead, a structure should be learned in an online manner. The online causal structure learning algorithms we present here can revise correlation values without reprocessing the entire dataset and use an existing model to avoid relearning the causal links in the prior model, which still fit data. Proposed algorithms are tested on synthetic and real-world datasets, the latter being a seasonally adjusted commodity price index dataset for the U.S. The online causal structure learning algorithms outperformed standard FCI by a large margin in learning the changed causal structure correctly and efficiently when latent variables were present.Comment: 16 pages, 9 figures, 2 table

Generating Outerplanar Graphs Uniformly at Random

This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.We show how to generate labelled and unlabelled outerplanar graphs with $n$ vertices uniformly at random in polynomial time in $n$. To generate labelled outerplanar graphs, we present a counting technique using the decomposition of a graph according to its block structure, and compute the exact number of labelled outerplanar graphs. This allows us to make the correct probabilistic choices in a recursive generation of uniformly distributed outerplanar graphs. Next we modify our formulas to also count rooted unlabelled graphs, and finally show how to use these formulas in a Las Vegas algorithm to generate unlabelled outerplanar graphs uniformly at random in expected polynomial time.Peer Reviewe