Related papers: Fast algorithm for generating ascending compositio…

An algorithm is given to factor an integer with $N$ digits in $\ln^m N$ steps, with $m$ approximately 4 or 5. Textbook quadratic sieve methods are exponentially slower. An improvement with the aid of an a particular function would provide a…

A novel integer sorting technique was proposed replacing bucket sort, distribution counting sort and address calculation sort family of algorithms which requires only constant amount of additional memory. The technique was inspired from one…

We present a new algorithm for iterating over all permutations of a sequence. The algorithm leverages elementary~$O(1)$ operations on recursive lists. As a result, no new nodes are allocated during the computation. Instead, all elements are…

For text retrieval systems, the assumption that all data structures reside in main memory is increasingly common. In this context, we present a novel incremental inverted indexing algorithm for web-scale collections that directly constructs…

Generating irreducible site-occupancy configurations by taking advantage of crystal symmetry is a ubiquitous method for accelerating of disordered structure prediction, which plays an important role in condensed matter physics and material…

We describe a generating tree approach to the enumeration and exhaustive generation of k-nonnesting set partitions and permutations. Unlike previous work in the literature using the connections of these objects to Young tableaux and…

Let $G$ be a finite group generated by $k$ elements. The well-known product replacement algorithm provides an effective method for sampling generating sets of $G$. We study a refinement of this algorithm that is designed to output…

We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…

In the work we discuss the benefit of using bitwise operations in programming. Some interesting examples in this respect have been shown. What is described in detail is an algorithm for sorting an integer array with the substantial use of…

We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such numbers in O(n^2.(log n)^(2+o(1))) bit-operations. We also give…

We provide a new framework for generating multiple good quality partitions (clusterings) of a single data set. Our approach decomposes this problem into two components, generating many high-quality partitions, and then grouping these…

Whilst there are perhaps only a few scientific methods, there seem to be almost as many artistic methods as there are artists. Artistic processes appear to inhabit the highest order of open-endedness. To begin to understand some of the…

Integer division instruction is generally expensive in most architectures. If the divisor is constant, the division can be transformed into combinations of several inexpensive integer instructions. This article discusses the classic…

We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…

Bringing high-level machine learning models to efficient and well-suited machine implementations often invokes a bunch of tools, e.g.~code generators, compilers, and optimizers. Along such tool chains, abstractions have to be applied. This…

This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…

The unit cost model is both convenient and largely realistic for describing integer decision algorithms over (+,*). Additional operations like division with remainder or bitwise conjunction, although equally supported by computing hardware,…

We give a new algorithm to construct optimal alphabetic ternary trees, where every internal node has at most three children. This algorithm generalizes the classic Hu-Tucker algorithm, though the overall computational complexity has yet to…

On common processors, integer multiplication is many times faster than integer division. Dividing a numerator n by a divisor d is mathematically equivalent to multiplication by the inverse of the divisor (n / d = n x 1/d). If the divisor is…

Many real-world problems require making sequences of decisions where the outcomes of each decision are probabilistic and uncertain, and the availability of different actions is constrained by the outcomes of previous actions. There is a…