Related papers: A Efficient Algorithm For Computing k-Factor

If K/k is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in K. The algorithm is flexible enough to find factors subject to additional…

Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…

Let K be a global field and f in K[X] be a polynomial. We present an efficient algorithm which factors f in polynomial time.

We present an algorithm producing all rational functions $f$ with prescribed $n+1$ Taylor coefficients at the origin and such that $\|f\|_\infty\le 1$ and $\deg f\le k$ for every fixed $k\ge n$. The case where $k<n$ is also discussed.

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…

While time complexity and space complexity of an algorithm helps to determine its efficiency when time or space needs to be optimized respectively, they fail to determine the more efficient algorithm when time and space both need to be…

The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…

The k Nearest Neighbors (kNN) method has received much attention in the past decades, where some theoretical bounds on its performance were identified and where practical optimizations were proposed for making it work fairly well in high…

We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…

We provide an elementary proof of a simple, efficient algorithm for computing the Euclidean projection of a point onto the probability simplex. We also show an application in Laplacian K-modes clustering.

We show that given the order of a single element selected uniformly at random from $\mathbb Z_N^*$, we can with very high probability, and for any integer $N$, efficiently find the complete factorization of $N$ in polynomial time. This…

We observe that successive applications of known results from the theory of positive systems lead to an {\it efficient general algorithm} for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one…

We review the X = K conjecture and important ingredients for the proof. We also attach notes on the rank estimate for the X = K theorem to hold and on the strange relation that was found to be valid without the assumption that the rank is…

We describe an efficient algorithm to compute finite type invariants of type $k$ by first creating, for a given knot $K$ with $n$ crossings, a look-up table for all subdiagrams of $K$ of size $\lceil \frac{k}{2}\rceil$ indexed by dyadic…

A strong direct product theorem says that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then our overall success probability will be exponentially small in k. We…

Fix a number field k. We prove that if there is an algorithm for deciding whether a smooth projective geometrically integral k-variety has a k-point, then there is an algorithm for deciding whether an arbitrary k-variety has a k-point and…

The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many…

We describe Universal Coefficient Theorems for the equivariant Kasparov theory for C*-algebras with an action of the group of integers or over a unique path space, using KK-valued invariants. We compare the resulting classification up to…

Capacitated k-median is one of the few outstanding optimization problems for which the existence of a polynomial time constant factor approximation algorithm remains an open problem. In a series of recent papers algorithms producing…

We prove in this paper that the expected value of the objective function of the $k$-means++ algorithm for samples converges to population expected value. As $k$-means++, for samples, provides with constant factor approximation for $k$-means…