scholarly journals Sampling-based approximate skyline calculation on big data

2021 ◽  
Author(s):  
Xingxing Xiao ◽  
Jianzhong Li
Keyword(s):  
Exact Solution ◽  
Big Data ◽  
Approximate Solution ◽  
Error Analysis ◽  
Linear Time ◽  
Approximate Algorithms ◽  
Skyline Query ◽  
Fixed Size ◽  
Skyline Queries ◽  
Input Size

Nowadays, big data is coming to the force in a lot of applications. Processing a skyline query on big data in more than linear time is by far too expensive and often even linear time may be too slow. It is obviously not possible to compute an exact solution to a skyline query in sublinear time, since an exact solution may itself have linear size. Fortunately, in many situations, a fast approximate solution is more useful than a slower exact solution. This paper proposes two sampling-based approximate algorithms for processing skyline queries. The first algorithm obtains a fixed size sample and computes the approximate skyline on it. The error of the algorithm is not only relatively small in most cases, but also is almost unaffected by the input size. The second algorithm returns an [Formula: see text]-approximation for the exact skyline efficiently. The running time of the algorithm has nothing to do with the input size in practical, achieving the goal of sublinearity on big data. Experiments verify the error analysis of the first algorithm, and show that the second is much faster than the existing skyline algorithms.

scholarly journals MapReduce Algorithm for Variants of Skyline Queries: Skyband and Dominating Queries

Algorithms ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 166
Author(s):  
Md. Anisuzzaman Siddique ◽  
Hao Tian ◽  
Mahboob Qaosar ◽  
Yasuhiko Morimoto
Keyword(s):  
Big Data ◽  
Knowledge Discovery ◽  
Distributed Environments ◽  
Skyline Query ◽  
Skyline Queries ◽  
Distributed Framework ◽  
Extensive Evaluation ◽  
Effectiveness And Efficiency ◽  
Synthetic Datasets ◽  
Better Than

The skyline query and its variant queries are useful functions in the early stages of a knowledge-discovery processes. The skyline query and its variant queries select a set of important objects, which are better than other common objects in the dataset. In order to handle big data, such knowledge-discovery queries must be computed in parallel distributed environments. In this paper, we consider an efficient parallel algorithm for the “K-skyband query” and the “top-k dominating query”, which are popular variants of skyline query. We propose a method for computing both queries simultaneously in a parallel distributed framework called MapReduce, which is a popular framework for processing “big data” problems. Our extensive evaluation results validate the effectiveness and efficiency of the proposed algorithm on both real and synthetic datasets.

scholarly journals A new approach for solving fractional RL circuit model through quadratic Legendre multi-wavelets

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Narottam Singh Chauhan
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Error Analysis ◽  
Classical Solution ◽  
Convergence Theorem ◽  
Fractional Integration ◽  
Approximate Solutions ◽  
Mean Square ◽  
Legendre Wavelets ◽  
New Approach

The aim of present work is to obtain the approximate solution of fractional model for the electrical RL circuit by using quadratic Legendre multiwavelet method (QLMWM). The beauty of the paper is convergence theorem and mean square error analysis, which shows that our approximate solution converges very rapidly to the exact solution and the numerical solution is compared with the classical solution and Legendre wavelets method (LWM) solution, which is much closer to the exact solution. The fractional integration is described in the Riemann-Liouville sense. The results are shows that the method is very effective and simple. In addition, using plotting tools, we compare approximate solutions of each equation with its classical solution and LWM .

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

scholarly journals Design and Analysis of Spatial Skyline Queries Indexing

2020 ◽  
Vol 9 (4S2) ◽  
pp. 23-29
Keyword(s):  
Current Practice ◽  
Dimensional Space ◽  
Information Age ◽  
Secondary Memory ◽  
Skyline Query ◽  
Skyline Queries ◽  
Keyword Query ◽  
Spatial Keyword Query ◽  
Nearest Points ◽  
The Ideal

Dwelling in the information age permits nearly everybody needs to recover countless information and choices to gather from to fulfill their necessities. In distinctive cases, the quantity of information accessible and the speed of change may cover the ideal and required explanation. Spatial-textual queries provide the most acclaimed nearest points concerning a conveyed site and a keyword set. Current practice regularly thought on the most capable technique to expertly get the top-k resultset reestablished a spatial-scholarly query. A capable Spatial Range Skyline Query (SRSQ) algorithm is proposed which initially performsa spatial keyword query (SKQ) that relies upon an IRtree that documents the information. Skyline centers picked are not simply established on their partitions to a lot of inquiries and more subject to their significance to a social occasion of query keywords. Additionally, besides proposed range skyline (RS) methods based on R-tree multi-dimensional space including secondary- memory pruning tools for operating field skyline queries is accomplished. The advanced scheme is dynamic and I/O optimum. Ultimately, methodology presents a modern assessment that demonstrates the proficiency.

Analysis of Deep Beams

1951 ◽  
Vol 18 (2) ◽  
pp. 163-172
Author(s):  
H. D. Conway ◽  
L. Chow ◽  
G. W. Morgan
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Stress Distribution ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Normal Stress ◽  
Stress Function ◽  
Beam Theory ◽  
Deep Beam ◽  
Stress Functions

Abstract This paper presents a method of analyzing the stress distribution in a deep beam of finite length by superimposing two stress functions. The first stress function is chosen in the form of a trigonometric series which satisfies all but one of the boundary conditions—that of zero normal stress on the ends of the beam. The principle of least work is then used to obtain a second stress function giving the distribution of normal stress on the ends which is left by the first stress function. By superimposing the two solutions, all the boundary conditions are satisfied. Two particular cases of a given type of loading are solved in this way to investigate the stresses in a deep beam and their deviation from the ordinary beam theory. In addition, an approximate solution by the numerical method of finite difference is worked out for one of the two cases. Results from the two methods are compared and discussed. A method of obtaining an exact solution to the problem is given in an Appendix.

On a new modified fractional analysis of Nagumo equation

2019 ◽  
Vol 12 (03) ◽  
pp. 1950034 ◽  
Author(s):  
Khaled M. Saad ◽  
Si̇nan Deni̇z ◽  
Dumi̇tru Baleanu
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Fractional Derivatives ◽  
Transform Method ◽  
Average Residual ◽  
Homotopy Analysis ◽  
Fractional Analysis ◽  
Nagumo Equation ◽  
Modified Equation

In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo–Fabrizio and Atangana–Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called [Formula: see text]-curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly.

scholarly journals Reproducing Kernel Method for Solving Nonlinear Fractional Fredholm Integrodifferential Equation

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Bothayna S. H. Kashkari ◽  
Muhammed I. Syam
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Integrodifferential Equation ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Integrodifferential Equations ◽  
Reproducing Kernel Method ◽  
Numerical Studies ◽  
Uniformly Convergence ◽  
Present Algorithm

This article is devoted to both theoretical and numerical studies of nonlinear fractional Fredholm integrodifferential equations. In this paper, we implement the reproducing kernel method (RKM) to approximate the solution of nonlinear fractional Fredholm integrodifferential equations. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the solution of the nonlinear fractional Fredholm integrodifferential equation. Uniformly convergence of the approximate solution produced by the RKM to the exact solution is proven.

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