Related papers: Fast algorithm for generating ascending compositio…

Projective Norms are a class of tensor norms that map on the input and output spaces. These norms are useful for providing a measure of entanglement. Calculating the projective norms is an NP-hard problem, which creates challenges in…

We present an algorithm for classification tasks on big data. Experiments conducted as part of this study indicate that the algorithm can be as accurate as ensemble methods such as random forests or gradient boosted trees. Unlike ensemble…

The data structure at the core of large-scale search engines is the inverted index, which is essentially a collection of sorted integer sequences called inverted lists. Because of the many documents indexed by such engines and stringent…

The basic result of this note is a statement about the existence of families of partitions of the set of natural numbers with some favourable properties, the n-optimal matrices of partitions. We use this to improve a decomposition result…

The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficient algorithm to compute…

An algorithm for the generation of shuttling sequences is necessary for the operation of a linear segmented ion-trap quantum computer. The present work provides an implementation of an algorithm that produces sequences proved to be optimal…

Generative 3D part assembly involves understanding part relationships and predicting their 6-DoF poses for assembling a realistic 3D shape. Prior work often focus on the geometry of individual parts, neglecting part-whole hierarchies of…

Numerous methods have been considered to create a fast integer factorization algorithm. Despite its apparent simplicity, the difficulty to find such an algorithm plays a crucial role in modern cryptography, notably, in the security of RSA…

Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper…

We propose a new method, probabilistic divide-and-conquer, for improving the success probability in rejection sampling. For the example of integer partitions, there is an ideal recursive scheme which improves the rejection cost from…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Compression algorithms are important for data oriented tasks, especially in the era of Big Data. Modern processors equipped with powerful SIMD instruction sets, provide us an opportunity for achieving better compression performance.…

Let A be a nonempty finite set of relatively prime positive integers, and let p_A(n) denote the number of partitions of n with parts in A. An elementary arithmetic argument is used to obtain an asymptotic formula for p_A(n).

In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…

We propose Composition Sampling, a simple but effective method to generate diverse outputs for conditional generation of higher quality compared to previous stochastic decoding strategies. It builds on recently proposed plan-based neural…

In the first place, a novel, yet straightforward in-place integer value-sorting algorithm is presented. It sorts in linear time using constant amount of additional memory for storing counters and indices beside the input array. The…

In real-life applications, most optimization problems are variants of well-known combinatorial optimization problems, including additional constraints to fit with a particular use case. Usually, efficient algorithms to handle a restricted…

This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…

In this article, we present a new algorithm for computing a generating set of a lattice ideal. This algorithm is based on a project-and-lift approach and is implemented in 4ti2. We also include a computational comparison of several existing…