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The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…
We propose a computational method to obtain series expansions in powers of time for general dynamical systems described by a set of hierarchical rate equations. The method is generally applicable to problems in both equilibrium and…
We consider the problem of augmenting an n-vertex graph embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present exact algorithms for the cases when (i) the input…
This paper presents an adaptation of recently developed algorithms for quadratic forms over number fields in arXiv:1304.0708 to global function fields of odd characteristics. First, we present algorithm for checking if a given…
A visibility algorithm maps time series into complex networks following a simple criterion. The resulting visibility graph has recently proven to be a powerful tool for time series analysis. However its straightforward computation is…
This paper develops a new class of algorithms for general linear systems and eigenvalue problems. These algorithms apply fast randomized sketching to accelerate subspace projection methods, such as GMRES and Rayleigh--Ritz. This approach…
The main results of this paper provide an Efficient Polynomial-Time Approximation Scheme (EPTAS) for approximating the genus (and non-orientable genus) of dense graphs. By dense we mean that $|E(G)|\ge \alpha |V(G)|^2$ for some fixed…
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…
We propose an approach to determine the continual progression of algorithmic efficiency, as an alternative to standard calculations of time complexity, likely, but not exclusively, when dealing with data structures with unknown maximum…
We present an efficient, trivially parallelizable algorithm to compute offset surfaces of shapes discretized using a dexel data structure. Our algorithm is based on a two-stage sweeping procedure that is simple to implement and efficient,…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
As computational astrophysics comes under pressure to become a precision science, there is an increasing need to move to high accuracy schemes for computational astrophysics. Hence the need for a specialized review on higher order schemes…
We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original…
In this letter we show how the method of [4] for the calculation of two-point functions in d+1-dimensional AdS space can be simplified. This results in an algorithm for the evaluation of the two-point functions as linear combinations of…
Computing fixed-radius near-neighbor graphs is an important first step for many data analysis algorithms. Near-neighbor graphs connect points that are close under some metric, endowing point clouds with a combinatorial structure. As…
This article presents an algorithm to compute digital images of Voronoi, Johnson-Mehl or Laguerre diagrams of a set of punctual sites, in a domain of a Euclidean space of any dimension. The principle of the algorithm is, in a first step, to…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
One fruitful formulation of Deep Networks (DNs) enabling their theoretical study and providing practical guidelines to practitioners relies on Piecewise Affine Splines. In that realm, a DN's input-mapping is expressed as per-region affine…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…
We study the exact counting problem for all lattice rectangles contained in the square $[0,n)\times[0,n)$, including non-axis-parallel ones. Starting from the standard parametrization by a primitive direction $(u,v)$ and two side lengths,…