Related papers: On the Average Runtime of an Open Source Binomial …
We present algorithms for generating small random samples without replacement. We consider two cases. We present an algorithm for sampling a pair of distinct integers, and an algorithm for sampling a triple of distinct integers. The…
Evolutionary algorithms rely very heavily on randomized behavior. Execution speed, therefore, depends strongly on how we implement randomness, such as our choice of pseudorandom number generator, or the algorithms used to map pseudorandom…
Byte Pair Encoding (BPE) is a widely used tokenization algorithm, whose tokens cannot extend across pre-tokenization boundaries, functionally limiting it to representing at most full words. The BoundlessBPE and SuperBPE algorithms extend…
We study the mixing time of the symmetric beta-binomial splitting process on finite weighted connected graphs $G=(V,E,\{r_e\}_{e\in E})$ with vertex set $V$, edge set $E$ and positive edge-weights $r_e>0$ for $e\in E$. This is an…
Tokenization is a critical preprocessing step in large language model pipelines, yet widely-used implementations remain CPU-bound and suboptimal for batch inference workflows on GPU. We present BlockBPE, a parallel GPU implementation of…
In simulations, probabilistic algorithms and statistical tests, we often generate random integers in an interval (e.g., [0,s)). For example, random integers in an interval are essential to the Fisher-Yates random shuffle. Consequently,…
A C library for random number generation, Randompack, is presented. The library implements several modern random number generators (engines), including xoshiro256, PCG64, Philox, ranlux++, and sfc64; 14 continuous distributions including…
Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE…
We present the first algorithm for generating random variates exactly uniformly from the set of perfect matchings of a bipartite graph with a polynomial expected running time over a nontrivial set of graphs. Previous Markov chain approaches…
We give an efficient algorithm to generate a graph from a distribution $\epsilon$-close to $G(n,p)$, in the sense of total variation distance. In particular, if $p$ is represented with $O(\log n)$-bit accuracy, then, with high probability,…
Random circuit sampling has become a popular means for demonstrating the superiority of quantum computers over classical supercomputers. While quantum chips are evolving rapidly, classical sampling algorithms are also getting better and…
Pseudorandom number generators are required for many computational tasks, such as stochastic modelling and simulation. This paper investigates the serial CPU and parallel GPU implementation of a Linear Congruential Generator based on the…
A method for generating random $U(1)$ variables with Boltzmann distribution is presented. It is based on the rejection method with transformation of variables. High efficiency is achieved for all range of temparatures or coupling…
We propose efficient techniques for generating independent identically distributed uniform random samples inside semialgebraic sets. The proposed algorithm leverages recent results on the approximation of indicator functions by polynomials…
Probabilistic breadth-first traversals (BPTs) are used in many network science and graph machine learning applications. In this paper, we are motivated by the application of BPTs in stochastic diffusion-based graph problems such as…
Counting the independent sets of a graph is a classical #P-complete problem, even in the bipartite case. We give an exponential-time approximation scheme for this problem which is faster than the best known algorithm for the exact problem.…
Version Control Systems, such as Git and Mercurial, manage the history of a project as a Directed Acyclic Graph encoding the various divergences and synchronizations happening in its life cycle. A popular workflow in the industry, called…
We introduce an algorithm for the uniform generation of infinite traces, i.e., infinite words up to commutation of some letters. The algorithm outputs on-the-fly approximations of a theoretical infinite trace, the latter being distributed…
Credal networks are a popular class of imprecise probabilistic graphical models obtained as a Bayesian network generalization based on, so-called credal, sets of probability mass functions. A Java library called CREMA has been recently…
We give a linear-time algorithm that approximately uniformly generates a random simple graph with a power-law degree sequence whose exponent is at least 2.8811. While sampling graphs with power-law degree sequence of exponent at least 3 is…