Search results for: θ -Euclidean k-fuzzy ideal.

Authors: R. K. Singh, P.K.Jain

Abstract:

Operating a device at high power and high frequency is a major problem because wall losses greatly reduce the efficiency of the device. In the present communication, authors analytically analyzed the dependence of ohmic/RF efficiency, the fraction of output power with respect to the total power generated, of gyrotron cavity structure on the conductivity of copper for the second harmonic TE0,6 mode. This study shows a rapid fall in the RF efficiency as the quality (conductivity) of copper degrades. Starting with an RF efficiency near 40% at the conductivity of ideal copper (5.8 x 107 S/m), the RF efficiency decreases (upto 8%) as the copper quality degrades. Assuming conductivity half that of ideal copper the RF efficiency as a function of diffractive quality factor, Qdiff, has been studied. Here the RF efficiency decreases rapidly with increasing diffractive Q. Ohmic wall losses as a function of frequency for 460 GHz gyrotron cavity excited in TE0,6 mode has also been analyzed. For 460 GHz cavity, the extracted power is reduced to 32% of the generated power due to ohmic losses in the walls of the cavity.

Keywords: Diffractive quality factor, Gyrotron, Ohmic wall losses, Open cavity resonator, RF Efficiency.

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Authors: C. Ardil

Abstract:

Multiple criteria decision making analysis (MCDMA) methods are applied to many real - life problems in different fields of engineering science and technology. The "preference analysis for reference ideal solution (PARIS)" method is proposed for an efficient MCDMA evaluation of decision problems. The multiple criteria aircraft evaluation approach is based on the integrated the mean weight, entropy weight, PARIS, and TOPSIS method, which eliminates the subjective importance weight assignment process. The evaluation criteria were identified from an extensive literature review of aircraft selection process. The aim of this study is to propose an efficient methodology for handling the aircraft selection process in which the proposed method solves effectively the MCDMA problem. A numerical example is presented to demonstrate the applicability and validity of the proposed MCDMA approach. 

Keywords: aircraft selection, aircraft, multiple criteria decision making, multiple criteria decision making analysis, mean weight, entropy weight, MCDMA, PARIS, TOPSIS, VIKOR, ELECTRE, PROMETHEE

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Authors: Omid Gervei, Ahmad Ayatollahi, Navid Gervei

Abstract:

In this paper we present an approach for 3D face recognition based on extracting principal components of range images by utilizing modified PCA methods namely 2DPCA and bidirectional 2DPCA also known as (2D) 2 PCA.A preprocessing stage was implemented on the images to smooth them using median and Gaussian filtering. In the normalization stage we locate the nose tip to lay it at the center of images then crop each image to a standard size of 100*100. In the face recognition stage we extract the principal component of each image using both 2DPCA and (2D) 2 PCA. Finally, we use Euclidean distance to measure the minimum distance between a given test image to the training images in the database. We also compare the result of using both methods. The best result achieved by experiments on a public face database shows that 83.3 percent is the rate of face recognition for a random facial expression.

Keywords: 3D face recognition, 2DPCA, (2D) 2 PCA, Rangeimage

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Authors: Hanan Mahmoud Ezzat Mahmoud, Alaa Abd El Fatah Hefnawy

Abstract:

In this paper, we present a system for content-based retrieval of large database of classified satellite images, based on user's relevance feedback (RF).Through our proposed system, we divide each satellite image scene into small subimages, which stored in the database. The modified radial basis functions neural network has important role in clustering the subimages of database according to the Euclidean distance between the query feature vector and the other subimages feature vectors. The advantage of using RF technique in such queries is demonstrated by analyzing the database retrieval results.

Keywords: content-based image retrieval, large database of image, RBF neural net, relevance feedback

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Authors: José M. Merigó, Anna M. Gil-Lafuente

Abstract:

Different types of aggregation operators such as the ordered weighted quasi-arithmetic mean (Quasi-OWA) operator and the normalized Hamming distance are studied. We introduce the use of the OWA operator in generalized distances such as the quasiarithmetic distance. We will call these new distance aggregation the ordered weighted quasi-arithmetic distance (Quasi-OWAD) operator. We develop a general overview of this type of generalization and study some of their main properties such as the distinction between descending and ascending orders. We also consider different families of Quasi-OWAD operators such as the Minkowski ordered weighted averaging distance (MOWAD) operator, the ordered weighted averaging distance (OWAD) operator, the Euclidean ordered weighted averaging distance (EOWAD) operator, the normalized quasi-arithmetic distance, etc.

Keywords: Aggregation operators, Distance measures, Quasi- OWA operator.

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Authors: Debashree Guha, Debjani Chakraborty

Abstract:

The aim of this paper is to adopt a compromise ratio (CR) methodology for fuzzy multi-attribute single-expert decision making proble. In this paper, the rating of each alternative has been described by linguistic terms, which can be expressed as triangular fuzzy numbers. The compromise ratio method for fuzzy multi-attribute single expert decision making has been considered here by taking the ranking index based on the concept that the chosen alternative should be as close as possible to the ideal solution and as far away as possible from the negative-ideal solution simultaneously. From logical point of view, the distance between two triangular fuzzy numbers also is a fuzzy number, not a crisp value. Therefore a fuzzy distance measure, which is itself a fuzzy number, has been used here to calculate the difference between two triangular fuzzy numbers. Now in this paper, with the help of this fuzzy distance measure, it has been shown that the compromise ratio is a fuzzy number and this eases the problem of the decision maker to take the decision. The computation principle and the procedure of the compromise ratio method have been described in detail in this paper. A comparative analysis of the compromise ratio method previously proposed [1] and the newly adopted method have been illustrated with two numerical examples.

Keywords: Compromise ratio method, Fuzzy multi-attributesingle-expert decision making, Fuzzy number, Linguistic variable

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Authors: C. Ardil

Abstract:

This article presents a multiple criteria evaluation approach to uncertainty, vagueness, and imprecision analysis for ranking alternatives with fuzzy data for decision making using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The fighter aircraft evaluation and selection decision making problem is modeled in a fuzzy environment with triangular fuzzy numbers. The fuzzy decision information related to the fighter aircraft selection problem is taken into account in ordering the alternatives and selecting the best candidate. The basic fuzzy TOPSIS procedure steps transform fuzzy decision matrices into matrices of alternatives evaluated according to all decision criteria. A practical numerical example illustrates the proposed approach to the fighter aircraft selection problem.

Keywords: triangular fuzzy number (TFN), multiple criteria decision making analysis, decision making, aircraft selection, MCDMA, fuzzy TOPSIS

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Authors: A. Borji, M. Hamidi

Abstract:

In this paper we examine the use of global texture analysis based approaches for the purpose of Persian font recognition in machine-printed document images. Most existing methods for font recognition make use of local typographical features and connected component analysis. However derivation of such features is not an easy task. Gabor filters are appropriate tools for texture analysis and are motivated by human visual system. Here we consider document images as textures and use Gabor filter responses for identifying the fonts. The method is content independent and involves no local feature analysis. Two different classifiers Weighted Euclidean Distance and SVM are used for the purpose of classification. Experiments on seven different type faces and four font styles show average accuracy of 85% with WED and 82% with SVM classifier over typefaces

Keywords: Persian font recognition, support vector machine, gabor filter.

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Authors: Neelima Gupta, Seema Aggarwal

Abstract:

Most of the biclustering/projected clustering algorithms are based either on the Euclidean distance or correlation coefficient which capture only linear relationships. However, in many applications, like gene expression data and word-document data, non linear relationships may exist between the objects. Mutual Information between two variables provides a more general criterion to investigate dependencies amongst variables. In this paper, we improve upon our previous algorithm that uses mutual information for biclustering in terms of computation time and also the type of clusters identified. The algorithm is able to find biclusters with mixed relationships and is faster than the previous one. To the best of our knowledge, none of the other existing algorithms for biclustering have used mutual information as a similarity measure. We present the experimental results on synthetic data as well as on the yeast expression data. Biclusters on the yeast data were found to be biologically and statistically significant using GO Tool Box and FuncAssociate.

Keywords: Biclustering, mutual information.

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Authors: S. Farahat, E. Khorasani Nejad, S. M. Hoseini Sarvari

Abstract:

In this paper multi-objective genetic algorithms are employed for Pareto approach optimization of ideal Turboshaft engines. In the multi-objective optimization a number of conflicting objective functions are to be optimized simultaneously. The important objective functions that have been considered for optimization are specific thrust (F/m& 0), specific fuel consumption ( P S ), output shaft power 0 (& /&) shaft W m and overall efficiency( ) O η . These objectives are usually conflicting with each other. The design variables consist of thermodynamic parameters (compressor pressure ratio, turbine temperature ratio and Mach number). At the first stage single objective optimization has been investigated and the method of NSGA-II has been used for multiobjective optimization. Optimization procedures are performed for two and four objective functions and the results are compared for ideal Turboshaft engine. In order to investigate the optimal thermodynamic behavior of two objectives, different set, each including two objectives of output parameters, are considered individually. For each set Pareto front are depicted. The sets of selected decision variables based on this Pareto front, will cause the best possible combination of corresponding objective functions. There is no superiority for the points on the Pareto front figure, but they are superior to any other point. In the case of four objective optimization the results are given in tables.

Keywords: Multi-objective, Genetic algorithm, Turboshaft Engine.

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Authors: C. S. Sastry, Saurabh Jain, Ashish Mishra

Abstract:

Image retrieval is a topic where scientific interest is currently high. The important steps associated with image retrieval system are the extraction of discriminative features and a feasible similarity metric for retrieving the database images that are similar in content with the search image. Gabor filtering is a widely adopted technique for feature extraction from the texture images. The recently proposed sparsity promoting l1-norm minimization technique finds the sparsest solution of an under-determined system of linear equations. In the present paper, the l1-norm minimization technique as a similarity metric is used in image retrieval. It is demonstrated through simulation results that the l1-norm minimization technique provides a promising alternative to existing similarity metrics. In particular, the cases where the l1-norm minimization technique works better than the Euclidean distance metric are singled out.

Keywords: l1-norm minimization, content based retrieval, modified Gabor function.

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Authors: Mahdi Shaneh, Azizollah Taheri

Abstract:

The goal of this project is to design a system to recognition voice commands. Most of voice recognition systems contain two main modules as follow “feature extraction" and “feature matching". In this project, MFCC algorithm is used to simulate feature extraction module. Using this algorithm, the cepstral coefficients are calculated on mel frequency scale. VQ (vector quantization) method will be used for reduction of amount of data to decrease computation time. In the feature matching stage Euclidean distance is applied as similarity criterion. Because of high accuracy of used algorithms, the accuracy of this voice command system is high. Using these algorithms, by at least 5 times repetition for each command, in a single training session, and then twice in each testing session zero error rate in recognition of commands is achieved.

Keywords: MFCC, Vector quantization, Vocal tract, Voicecommand.

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Authors: C. Pislaru, A. Shebani

Abstract:

This paper uses the radial basis function neural network (RBFNN) for system identification of nonlinear systems. Five nonlinear systems are used to examine the activity of RBFNN in system modeling of nonlinear systems; the five nonlinear systems are dual tank system, single tank system, DC motor system, and two academic models. The feed forward method is considered in this work for modelling the non-linear dynamic models, where the KMeans clustering algorithm used in this paper to select the centers of radial basis function network, because it is reliable, offers fast convergence and can handle large data sets. The least mean square method is used to adjust the weights to the output layer, and Euclidean distance method used to measure the width of the Gaussian function.

Keywords: System identification, Nonlinear system, Neural networks, RBF neural network.

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Authors: C. Ardil

Abstract:

The purpose of this paper is to present fuzzy TOPSIS in an entropic fuzzy environment. Due to the ambiguous concepts often represented in decision data, exact values are insufficient to model real-life situations. In this paper, the rating of each alternative is defined in fuzzy linguistic terms, which can be expressed with triangular fuzzy numbers. The weight of each criterion is then derived from the decision matrix using the entropy weighting method. Next, a vertex method is proposed to calculate the distance between two triangular fuzzy numbers. According to the TOPSIS concept, a closeness coefficient is defined to determine the ranking order of all alternatives by simultaneously calculating the distances to both the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS). Finally, an illustrative example of selecting stealth fighter aircraft is shown at the end of this article to highlight the procedure of the proposed method. Correlation analysis and validation analysis using TOPSIS, WSM, and WPM methods were performed to compare the ranking order of the alternatives.

Keywords: stealth fighter aircraft selection, fuzzy uncertainty theory (FUT), fuzzy entropic decision (FED), fuzzy linguistic variables, triangular fuzzy numbers, multiple criteria decision making analysis, MCDMA, TOPSIS, WSM, WPM

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Authors: Y. Wang

Abstract:

The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is O(CN_maxn²) where C is the iterations, N_max is the maximum number of frequency quadrilaterals containing each edge and n is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5n edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.

Keywords: Frequency quadrilateral, iterative algorithm, sparse graph, traveling salesman problem.

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Authors: Abdellatif Kasbi, Abderrafii Rahali

Abstract:

In an electric power grid connected wind generation system, dynamic control strategy is essential to use the wind energy efficiently as well as for an energy optimization. The present study has focused on decoupled power regulation of doubly fed induction generator, operating in wind turbine, in accordance with the vector control approach by applying fractional order proportional integral (FOPI) controller. The FOPI controller is designed based on a simple method; up such that the response of closed loop process is similar to the response of a specified fractional model whose transfer function is Bode’s ideal function. In this tuning operation, the parameters of the proposed fractional controller are established analytically using the impulse closed-loop response of the controlled process. To show the superior action of the developed FOPI controller in comparison with standard PI controller in different function conditions, the study is validated through simulation using the software MATLAB/Simulink.

Keywords: Wind generation system, DFIG, vector control approach, fractional order PI controller, Bode’s ideal transfer function, impulse response.

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Authors: Nor Azuana Ramli, Mohd Tahir Ismail, Hooy Chee Wooi

Abstract:

Developing a stable early warning system (EWS) model that is capable to give an accurate prediction is a challenging task. This paper introduces k-nearest neighbour (k-NN) method which never been applied in predicting currency crisis before with the aim of increasing the prediction accuracy. The proposed k-NN performance depends on the choice of a distance that is used where in our analysis; we take the Euclidean distance and the Manhattan as a consideration. For the comparison, we employ three other methods which are logistic regression analysis (logit), back-propagation neural network (NN) and sequential minimal optimization (SMO). The analysis using datasets from 8 countries and 13 macro-economic indicators for each country shows that the proposed k-NN method with k = 4 and Manhattan distance performs better than the other methods.

Keywords: Currency crisis, k-nearest neighbour method, logit, neural network.

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Authors: A. Hasankhani, H. Saadat, M. M. Zahedi

Abstract:

In this paper some properties of the uniformity topology on a BCI-algebras are discussed.

Keywords: (Fuzzy) ideal, (Fuzzy) subalgebra, Uniformity, clopen sets.

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Authors: Irene Luque Ruiz, Manuel Urbano Cuadrado, Miguel Ángel Gómez-Nieto

Abstract:

In this paper we study different similarity based approaches for the development of QSAR model devoted to the prediction of activity of antiobesity drugs. Classical similarity approaches are compared regarding to dissimilarity models based on the consideration of the calculation of Euclidean distances between the nonisomorphic fragments extracted in the matching process. Combining the classical similarity and dissimilarity approaches into a new similarity measure, the Approximate Similarity was also studied, and better results were obtained. The application of the proposed method to the development of quantitative structure-activity relationships (QSAR) has provided reliable tools for predicting of inhibitory activity of drugs. Acceptable results were obtained for the models presented here.

Keywords: Graph similarity, Nonisomorphic dissimilarity, Approximate similarity, Drugs activity prediction.

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Authors: Atef. A. Ata, Sohair F. Rezeka, Ahmed El-Shenawy, Mohammed Diab

Abstract:

Image processing in today’s world grabs massive attentions as it leads to possibilities of broaden application in many fields of high technology. The real challenge is how to improve existing sorting system applications which consists of two integrated stations of processing and handling with a new image processing feature. Existing color sorting techniques use a set of inductive, capacitive, and optical sensors to differentiate object color. This research presents a mechatronic color sorting system solution with the application of image processing. A 5-DOF robot arm is designed and developed with pick and place operation to act as the main part of the color sorting system. Image processing procedure senses the circular objects in an image captured in real time by a webcam fixed at the end-effector then extracts color and position information out of it. This information is passed as a sequence of sorting commands to the manipulator that has pick-and-place mechanism. Performance analysis proves that this color based object sorting system works accurately under ideal condition in term of adequate illumination, circular objects shape and color. The circular objects tested for sorting are red, green and blue. For non-ideal condition, such as unspecified color the accuracy reduces to 80%.

Keywords: Robotics manipulator, 5-DOF manipulator, image processing, Color sorting, Pick-and-place.

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Authors: F. Rotaru, S. Bejinariu, C. D. Niţâ, R. Luca, I. Pâvâloi, C. Lazâr

Abstract:

The paper presents a technique suitable in robot vision applications where it is not possible to establish the object position from one view. Usually, one view pose calculation methods are based on the correspondence of image features established at a training step and exactly the same image features extracted at the execution step, for a different object pose. When such a correspondence is not feasible because of the lack of specific features a new method is proposed. In the first step the method computes from two views the 3D pose of feature points. Subsequently, using a registration algorithm, the set of 3D feature points extracted at the execution phase is aligned with the set of 3D feature points extracted at the training phase. The result is a Euclidean transform which have to be used by robot head for reorientation at execution step.

Keywords: features correspondence, registration algorithm, robot vision, triangulation method.

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Authors: Samira Malekmohammadi Golsefid, Mehdi Ghazanfari, Somayeh Alizadeh

Abstract:

The goal of this paper is to segment the countries based on the value of export from Iran during 14 years ending at 2005. To measure the dissimilarity among export baskets of different countries, we define Dissimilarity Export Basket (DEB) function and use this distance function in K-means algorithm. The DEB function is defined based on the concepts of the association rules and the value of export group-commodities. In this paper, clustering quality function and clusters intraclass inertia are defined to, respectively, calculate the optimum number of clusters and to compare the functionality of DEB versus Euclidean distance. We have also study the effects of importance weight in DEB function to improve clustering quality. Lastly when segmentation is completed, a designated RFM model is used to analyze the relative profitability of each cluster.

Keywords: Customers segmentation, Customer relationship management, Clustering, Data Mining

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Authors: Marios Poulos, Sozon Papavlasopoulos, V. S. Belesiotis

Abstract:

In the proposed method for Web page-ranking, a novel theoretic model is introduced and tested by examples of order relationships among IP addresses. Ranking is induced using a convexity feature, which is learned according to these examples using a self-organizing procedure. We consider the problem of selforganizing learning from IP data to be represented by a semi-random convex polygon procedure, in which the vertices correspond to IP addresses. Based on recent developments in our regularization theory for convex polygons and corresponding Euclidean distance based methods for classification, we develop an algorithmic framework for learning ranking functions based on a Computational Geometric Theory. We show that our algorithm is generic, and present experimental results explaining the potential of our approach. In addition, we explain the generality of our approach by showing its possible use as a visualization tool for data obtained from diverse domains, such as Public Administration and Education.

Keywords: Computational Geometry, Education, e-Governance, Semantic Web.

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Authors: Ali Ganoun

Abstract:

This paper proposes evaluation of sound parameterization methods in recognizing some spoken Arabic words, namely digits from zero to nine. Each isolated spoken word is represented by a single template based on a specific recognition feature, and the recognition is based on the Euclidean distance from those templates. The performance analysis of recognition is based on four parameterization features: the Burg Spectrum Analysis, the Walsh Spectrum Analysis, the Thomson Multitaper Spectrum Analysis and the Mel Frequency Cepstral Coefficients (MFCC) features. The main aim of this paper was to compare, analyze, and discuss the outcomes of spoken Arabic digits recognition systems based on the selected recognition features. The results acqired confirm that the use of MFCC features is a very promising method in recognizing Spoken Arabic digits.

Keywords: Speech Recognition, Spectrum Analysis, Burg Spectrum, Walsh Spectrum Analysis, Thomson Multitaper Spectrum, MFCC.

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Authors: J. Yang, Y. Ma, X. Zhang, S. Li, Y. Zhang

Abstract:

The traditional k-means algorithm has been widely used as a simple and efficient clustering method. However, the algorithm often converges to local minima for the reason that it is sensitive to the initial cluster centers. In this paper, an algorithm for selecting initial cluster centers on the basis of minimum spanning tree (MST) is presented. The set of vertices in MST with same degree are regarded as a whole which is used to find the skeleton data points. Furthermore, a distance measure between the skeleton data points with consideration of degree and Euclidean distance is presented. Finally, MST-based initialization method for the k-means algorithm is presented, and the corresponding time complexity is analyzed as well. The presented algorithm is tested on five data sets from the UCI Machine Learning Repository. The experimental results illustrate the effectiveness of the presented algorithm compared to three existing initialization methods.

Keywords: Degree, initial cluster center, k-means, minimum spanning tree.

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Authors: Shaoquan Sun, Qianqian Li

Abstract:

The aim of this paper is to introduce the notions of intuitionistic T-S fuzzy subalgebras and intuitionistic T-S fuzzy ideals in BCI-algebras, and then to investigate their basic properties.

Keywords: BCI-algebra, intuitionistic T-S fuzzy subalgebra, intuitionistic T-S fuzzy ideal, norm intersection, direct product, epimorphism, isomorphism.

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Authors: Iqbalur Rahman, Miftahur Rahman, Abul L Haque, Mostafizur Rahman,

Abstract:

In this paper, RSA encryption algorithm and its hardware implementation in Xilinx-s Virtex Field Programmable Gate Arrays (FPGA) is analyzed. The issues of scalability, flexible performance, and silicon efficiency for the hardware acceleration of public key crypto systems are being explored in the present work. Using techniques based on the interleaved math for exponentiation, the proposed RSA calculation architecture is compared to existing FPGA-based solutions for speed, FPGA utilization, and scalability. The paper covers the RSA encryption algorithm, interleaved multiplication, Miller Rabin algorithm for primality test, extended Euclidean math, basic FPGA technology, and the implementation details of the proposed RSA calculation architecture. Performance of several alternative hardware architectures is discussed and compared. Finally, conclusion is drawn, highlighting the advantages of a fully flexible & parameterized design.

Keywords: Crypto Accelerator, FPGA, Public Key Cryptography, RSA.

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Authors: S.K.Sardar, B.Davvaz, S.Kayal, S.K.Majumdar

Abstract:

The purpose of this note is to obtain some properties of (∈,∈ ∨q)- fuzzy bi-ideals in a Γ-semigroup in order to characterize regular and intra-regular Γ-semigroups.

Keywords: Regular Γ-semigroup, belong to or quasi-coincident, (∈, ∈ ∨q)-fuzzy subsemigroup, (∈, ∈ ∨q)-fuzzy bi-ideals.

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Authors: Zhoucheng Bao, Haiyan Zhu, Tingting Pang, Zuling Wang

Abstract:

This paper presents a multi population Differential Evolution (DE) with adaptive mutation and local search for global optimization, named AMMADE in order to better coordinate the cooperation between the populations and the rational use of resources. In AMMADE, the population is divided based on the Euclidean distance sorting method at each generation to appropriately coordinate the cooperation between subpopulations and the usage of resources, such that the best-performed subpopulation will get more computing resources in the next generation. Further, an adaptive local search strategy is employed on the best-performed subpopulation to achieve a balanced search. The proposed algorithm has been tested by solving optimization problems taken from CEC2014 benchmark problems. Experimental results show that our algorithm can achieve a competitive or better result than related methods. The results also confirm the significance of devised strategies in the proposed algorithm.

Keywords: Differential evolution, multi-mutation strategies, memetic algorithm, adaptive local search.

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Authors: Miloš Šeda

Abstract:

Finding the shortest path between two positions is a fundamental problem in transportation, routing, and communications applications. In robot motion planning, the robot should pass around the obstacles touching none of them, i.e. the goal is to find a collision-free path from a starting to a target position. This task has many specific formulations depending on the shape of obstacles, allowable directions of movements, knowledge of the scene, etc. Research of path planning has yielded many fundamentally different approaches to its solution, mainly based on various decomposition and roadmap methods. In this paper, we show a possible use of visibility graphs in point-to-point motion planning in the Euclidean plane and an alternative approach using Voronoi diagrams that decreases the probability of collisions with obstacles. The second application area, investigated here, is focused on problems of finding minimal networks connecting a set of given points in the plane using either only straight connections between pairs of points (minimum spanning tree) or allowing the addition of auxiliary points to the set to obtain shorter spanning networks (minimum Steiner tree).

Keywords: motion planning, spanning tree, Steiner tree, Delaunay triangulation, Voronoi diagram.

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