Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 14

Approximation Related Publications

14 Aggregation Scheduling Algorithms in Wireless Sensor Networks

Authors: Min Kyung An

Abstract:

In Wireless Sensor Networks which consist of tiny wireless sensor nodes with limited battery power, one of the most fundamental applications is data aggregation which collects nearby environmental conditions and aggregates the data to a designated destination, called a sink node. Important issues concerning the data aggregation are time efficiency and energy consumption due to its limited energy, and therefore, the related problem, named Minimum Latency Aggregation Scheduling (MLAS), has been the focus of many researchers. Its objective is to compute the minimum latency schedule, that is, to compute a schedule with the minimum number of timeslots, such that the sink node can receive the aggregated data from all the other nodes without any collision or interference. For the problem, the two interference models, the graph model and the more realistic physical interference model known as Signal-to-Interference-Noise-Ratio (SINR), have been adopted with different power models, uniform-power and non-uniform power (with power control or without power control), and different antenna models, omni-directional antenna and directional antenna models. In this survey article, as the problem has proven to be NP-hard, we present and compare several state-of-the-art approximation algorithms in various models on the basis of latency as its performance measure.

Keywords: Approximation, data aggregation, Interference, omni-directional, convergecast, gathering, directional

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13 Application of Method of Symmetries at a Calculation and Planning of Circular Plate with Variable Thickness

Authors: Kirill Trapezon, Alexandr Trapezon

Abstract:

A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: Approximation, vibrations, Symmetry‎, Plate, thickness, factorization

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12 Variational Evolutionary Splines for Solving a Model of Temporomandibular Disorders

Authors: Alberto Hananel

Abstract:

The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: Approximation, evolutionary PDE, temporomandibular disorders, variational spline, finite element method

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11 Efficient Broadcasting in Wireless Sensor Networks

Authors: Min Kyung An, Hyuk Cho

Abstract:

In this paper, we study the Minimum Latency Broadcast Scheduling (MLBS) problem in wireless sensor networks (WSNs). The main issue of the MLBS problem is to compute schedules with the minimum number of timeslots such that a base station can broadcast data to all other sensor nodes with no collisions. Unlike existing works that utilize the traditional omni-directional WSNs, we target the directional WSNs where nodes can collaboratively determine and orientate their antenna directions. We first develop a 7-approximation algorithm, adopting directional WSNs. Our ratio is currently the best, to the best of our knowledge. We then validate the performance of the proposed algorithm through simulation.

Keywords: Wireless Sensor Networks, Approximation, broadcast, collision-free, directional antenna

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10 Data Collection with Bounded-Sized Messages in Wireless Sensor Networks

Authors: Min Kyung An

Abstract:

In this paper, we study the data collection problem in Wireless Sensor Networks (WSNs) adopting the two interference models: The graph model and the more realistic physical interference model known as Signal-to-Interference-Noise-Ratio (SINR). The main issue of the problem is to compute schedules with the minimum number of timeslots, that is, to compute the minimum latency schedules, such that data from every node can be collected without any collision or interference to a sink node. While existing works studied the problem with unit-sized and unbounded-sized message models, we investigate the problem with the bounded-sized message model, and introduce a constant factor approximation algorithm. To the best known of our knowledge, our result is the first result of the data collection problem with bounded-sized model in both interference models.

Keywords: Wireless Sensor Networks, Approximation, data collection, WSN, SINR, collision-free, interference-free, physical interference model, bounded-sized message model

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9 Exploring Counting Methods for the Vertices of Certain Polyhedra with Uncertainties

Authors: Sammani Danwawu Abdullahi

Abstract:

Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.

Keywords: Mathematical Programming, Optimization, Approximation, counting with uncertainties, vertex enumeration

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8 An Approximation of Daily Rainfall by Using a Pixel Value Data Approach

Authors: Sarisa Pinkham, Kanyarat Bussaban

Abstract:

The research aims to approximate the amount of daily rainfall by using a pixel value data approach. The daily rainfall maps from the Thailand Meteorological Department in period of time from January to December 2013 were the data used in this study. The results showed that this approach can approximate the amount of daily rainfall with RMSE=3.343.

Keywords: Image Processing, Approximation, daily rainfall, pixel value data

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7 Minimization Problems for Generalized Reflexive and Generalized Anti-Reflexive Matrices

Authors: Yongxin Yuan

Abstract:

Let R ∈ Cm×m and S ∈ Cn×n be nontrivial unitary involutions, i.e., RH = R = R−1 = ±Im and SH = S = S−1 = ±In. A ∈ Cm×n is said to be a generalized reflexive (anti-reflexive) matrix if RAS = A (RAS = −A). Let ρ be the set of m × n generalized reflexive (anti-reflexive) matrices. Given X ∈ Cn×p, Z ∈ Cm×p, Y ∈ Cm×q and W ∈ Cn×q, we characterize the matrices A in ρ that minimize AX−Z2+Y HA−WH2, and, given an arbitrary A˜ ∈ Cm×n, we find a unique matrix among the minimizers of AX − Z2 + Y HA − WH2 in ρ that minimizes A − A˜. We also obtain sufficient and necessary conditions for existence of A ∈ ρ such that AX = Z, Y HA = WH, and characterize the set of all such matrices A if the conditions are satisfied. These results are applied to solve a class of left and right inverse eigenproblems for generalized reflexive (anti-reflexive) matrices.

Keywords: Approximation, Inverse eigenvalue problem, generalized reflexive matrix, generalized anti-reflexive matrix

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6 Generalization Kernel for Geopotential Approximation by Harmonic Splines

Authors: Elena Kotevska

Abstract:

This paper presents a generalization kernel for gravitational potential determination by harmonic splines. It was shown in [10] that the gravitational potential can be approximated using a kernel represented as a Newton integral over the real Earth body. On the other side, the theory of geopotential approximation by harmonic splines uses spherically oriented kernels. The purpose of this paper is to show that in the spherical case both kernels have the same type of representation, which leads us to conclusion that it is possible to consider the kernel represented as a Newton integral over the real Earth body as a kind of generalization of spherically harmonic kernels to real geometries.

Keywords: Approximation, reproducing kernel, Geopotential, Regular Surface

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5 An Empirical Validation of the Linear- Hyperbolic Approximation of the I-V Characteristic of a Solar Cell Generator

Authors: A. A. Penin

Abstract:

An empirical linearly-hyperbolic approximation of the I - V characteristic of a solar cell is presented. This approximation is based on hyperbolic dependence of a current of p-n junctions on voltage for large currents. Such empirical approximation is compared with the early proposed formal linearly-hyperbolic approximation of a solar cell. The expressions defining laws of change of parameters of formal approximation at change of a photo current of family of characteristics are received. It allows simplifying a finding of parameters of approximation on actual curves, to specify their values. Analytical calculation of load regime for linearly - hyperbolic model leads to quadratic equation. Also, this model allows to define soundly a deviation from the maximum power regime and to compare efficiency of regimes of solar cells with different parameters.

Keywords: Approximation, a solar cell generator, I − V characteristic, p − n junction

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4 A Discretizing Method for Reliability Computation in Complex Stress-strength Models

Authors: Alessandro Barbiero

Abstract:

This paper proposes, implements and evaluates an original discretization method for continuous random variables, in order to estimate the reliability of systems for which stress and strength are defined as complex functions, and whose reliability is not derivable through analytic techniques. This method is compared to other two discretizing approaches appeared in literature, also through a comparative study involving four engineering applications. The results show that the proposal is very efficient in terms of closeness of the estimates to the true (simulated) reliability. In the study we analyzed both a normal and a non-normal distribution for the random variables: this method is theoretically suitable for each parametric family.

Keywords: Approximation, Experimental Design, Monte Carlo simulations, asymmetry, interference theory

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3 Applications of Rough Set Decompositions in Information Retrieval

Authors: Chen Wu, Xiaohua Hu

Abstract:

This paper proposes rough set models with three different level knowledge granules in incomplete information system under tolerance relation by similarity between objects according to their attribute values. Through introducing dominance relation on the discourse to decompose similarity classes into three subclasses: little better subclass, little worse subclass and vague subclass, it dismantles lower and upper approximations into three components. By using these components, retrieving information to find naturally hierarchical expansions to queries and constructing answers to elaborative queries can be effective. It illustrates the approach in applying rough set models in the design of information retrieval system to access different granular expanded documents. The proposed method enhances rough set model application in the flexibility of expansions and elaborative queries in information retrieval.

Keywords: Approximation, Decomposition, dominance relation, Incomplete information system, Rough set model, tolerance relation, elaborative query

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2 Numerical Solution of Infinite Boundary Integral Equation by Using Galerkin Method with Laguerre Polynomials

Authors: N. M. A. Nik Long, Z. K. Eshkuvatov, M. Yaghobifar, M. Hasan

Abstract:

In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.

Keywords: Approximation, Galerkin Method, Integral equations, Laguerre polynomial

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1 Development of Machinable Ellipses by NURBS Curves

Authors: Yuan L. Lai, Jui P. Hung, Jian H. Chen

Abstract:

Owning to the high-speed feed rate and ultra spindle speed have been used in modern machine tools, the tool-path generation plays a key role in the successful application of a High-Speed Machining (HSM) system. Because of its importance in both high-speed machining and tool-path generation, approximating a contour by NURBS format is a potential function in CAD/CAM/CNC systems. It is much more convenient to represent an ellipse by parametric form than to connect points laboriously determined in a CNC system. A new approximating method based on optimum processes and NURBS curves of any degree to the ellipses is presented in this study. Such operations can be the foundation of tool-radius compensation interpolator of NURBS curves in CNC system. All operating processes for a CAD tool is presented and demonstrated by practical models.

Keywords: Approximation, optimum, ellipse, NURBS

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