Related papers: Classic Round-Up Variant of Fast Unsigned Division…
We present ${\rm poly\log\log n}$-round randomized distributed algorithms to compute vertex splittings, a partition of the vertices of a graph into $k$ parts such that a node of degree $d(u)$ has $\approx d(u)/k$ neighbors in each part. Our…
Some recent processors are not equipped with an integer division unit. Compilers then implement division by a call to a special function supplied by the processor designers, which implements division by a loop producing one bit of quotient…
Methods for generating new distributions from old can be thought of as techniques for simplifying integrals used in reverse. Hence integrating a probability density function (pdf) by parts provides a new way of modifying distributions; the…
We continue the study of statistical/computational tradeoffs in learning robust classifiers, following the recent work of Bubeck, Lee, Price and Razenshteyn who showed examples of classification tasks where (a) an efficient robust…
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…
Fully automated verification of concurrent programs is a difficult problem, primarily because of state explosion: the exponential growth of a program state space with the number of its concurrently active components. It is natural to apply…
Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. Many algorithms exist to generate all descending compositions, yet none have previously been published to generate…
Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…
We present several elementary closed-forms that express a non-trivial divisor for every composite integer $n > 1$. Each closed-form consists of a fixed number of elementary arithmetic operations drawn from the set: addition, subtraction,…
Ongoing efforts that span over decades show a rise of AI methods for accelerating scientific discovery, yet accelerating discovery in mathematics remains a persistent challenge for AI. Specifically, AI methods were not effective in creation…
Subset Sum is a classical optimization problem taught to undergraduates as an example of an NP-hard problem, which is amenable to dynamic programming, yielding polynomial running time if the input numbers are relatively small. Formally,…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
How to handle division in systems that compute with logical formulas involving what would otherwise be polynomial constraints over the real numbers is a surprisingly difficult question. This paper argues that existing approaches from both…
Stratified sampling is a fast and simple method to generate point sets with uniform distribution in hypercubes. However, for the most common paraxial stratfication it has the prominent drawback that the number of sampled points in n…
Partitioning a set of elements into an unknown number of mutually exclusive subsets is essential in many machine learning problems. However, assigning elements, such as samples in a dataset or neurons in a network layer, to an unknown and…
This paper proposes sufficient, yet more general conditions for applying FastTwoSum as an error-free transformation (EFT) under all faithful rounding modes. Additionally, it also identifies guarantees tailored to round-to-odd for…
Repeated recursion unfolding is a new approach that repeatedly unfolds a recursion with itself and simplifies it while keeping all unfolded rules. Each unfolding doubles the number of recursive steps covered. This reduces the number of…
The standard procedure when evaluating integrals of a given family of Feynman integrals, corresponding to some Feynman graph, is to construct an algorithm which provides the possibility to write any particular integral as a linear…
In applications of distributed storage systems to distributed computing and implementation of key- value stores, the following property, usually referred to as consistency in computer science and engineering, is an important requirement: as…
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…