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Related papers: Efficient Algorithms for Zeckendorf Arithmetic

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We propose an efficient linear-time graph-based divisive cluster analysis approach called Reductive Clustering. The approach tries to reveal the hierarchical structural information through reducing the graph into a more concise one…

Artificial Intelligence · Computer Science 2020-09-28 Ching Tarn , Yinan Zhang , Ye Feng

A 1-period is a complex number given by the integral of a univariate algebraic function, where all data involved -- the integrand and the domain of integration -- are defined over algebraic numbers. We give an algorithm that, given a finite…

Algebraic Geometry · Mathematics 2025-05-28 Emre Can Sertöz , Joël Ouaknine , James Worrell

In this paper we analyze the computational costs of various operations and algorithms in algebraic number fields using exact arithmetic. Let $K$ be an algebraic number field. In the first half of the paper, we calculate the running time and…

Symbolic Computation · Computer Science 2020-11-09 M. J. Uray

We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…

Quantum Physics · Physics 2019-03-14 Pablo Arrighi , Gilles Dowek

Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…

Optimization and Control · Mathematics 2023-07-10 Didier Chételat , Andrea Lodi

We introduce an efficient combination of polyhedral analysis and predicate partitioning. Template polyhedral analysis abstracts numerical variables inside a program by one polyhedron per control location, with a priori fixed directions for…

Logic in Computer Science · Computer Science 2014-10-06 David Monniaux , Peter Schrammel

We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…

Data Structures and Algorithms · Computer Science 2019-07-24 Sankardeep Chakraborty , Kunihiko Sadakane , Srinivasa Rao Satti

We consider two kinds of problems: the computation of polynomial and rational solutions of linear recurrences with coefficients that are polynomials with integer coefficients; indefinite and definite summation of sequences that are…

Symbolic Computation · Computer Science 2008-04-03 Alin Bostan , Frédéric Chyzak , Bruno Salvy , Thomas Cluzeau

We tackle the issue of representing infinite sets of real- valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our…

Logic in Computer Science · Computer Science 2008-12-11 Florent Bouchy , Alain Finkel , Jérôme Leroux

We present two new algorithms for the computation of the q-integer linear decomposition of a multivariate polynomial. Such a decomposition is essential for the treatment of q-hypergeometric symbolic summation via creative telescoping and…

Symbolic Computation · Computer Science 2021-02-15 Mark Giesbrecht , Hui Huang , George Labahn , Eugene Zima

The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our…

Data Structures and Algorithms · Computer Science 2019-06-05 Monika Henzinger , Alexander Noe , Christian Schulz , Darren Strash

Zeckendorf's Theorem states that any positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers. We consider higher-dimensional lattice analogues, where a legal decomposition of a number $n$ is a collection of…

Number Theory · Mathematics 2018-09-18 Eric Chen , Robin Chen , Lucy Guo , Cindy Jiang , Steven J. Miller , Joshua M. Siktar , Peter Yu

Two widely-used computational paradigms for sublinear algorithms are using linear measurements to perform computations on a high dimensional input and using structured queries to access a massive input. Typically, algorithms in the former…

Computational Complexity · Computer Science 2021-07-14 Amit Chakrabarti , Manuel Stoeckl

Temporal networks model a variety of important phenomena involving timed interactions between entities. Existing methods for machine learning on temporal networks generally exhibit at least one of two limitations. First, time is assumed to…

Machine Learning · Computer Science 2022-10-04 Sudhanshu Chanpuriya , Ryan A. Rossi , Sungchul Kim , Tong Yu , Jane Hoffswell , Nedim Lipka , Shunan Guo , Cameron Musco

The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be…

Optimization and Control · Mathematics 2018-02-07 Johan Karlsson , Axel Ringh

Digital System Research has pioneered the mathematics and design for a new class of computing machine using residue numbers. Unlike prior art, the new breakthrough provides methods and apparatus for general purpose computation using several…

Other Computer Science · Computer Science 2015-12-04 Eric B. Olsen

The following two decision problems capture the complexity of comparing integers or rationals that are succinctly represented in product-of-exponentials notation, or equivalently, via arithmetic circuits using only multiplication and…

Computational Complexity · Computer Science 2014-04-08 Kousha Etessami , Alistair Stewart , Mihalis Yannakakis

We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes involve complex…

Numerical Analysis · Mathematics 2023-06-01 Joackim Bernier , Sergio Blanes , Fernando Casas , Alejandro Escorihuela-Tomàs

This paper describes an approach to computer aided calculations in the cohomology of arithmetic groups. It complements existing literature on the topic by emphasizing homotopies and perturbation techniques, rather than cellular subdivision,…

Number Theory · Mathematics 2025-08-26 Graham Ellis

We apply some recent developments of Baldoni-Beck-Cochet-Vergne on vector partition function, to Kostant's and Steinberg's formulae, for classical Lie algebras $A\_r$, $B\_r$, $C\_r$, $D\_r$. We therefore get efficient {\tt Maple} programs…

Representation Theory · Mathematics 2009-09-29 Charles Cochet