An Analysis of a Recursive and an Iterative Algorithm for Generating Permutations Modified for Travelling Salesman Problem

This paper presents the results of a comparative analysis between a recursive and an iterative algorithm when generating permutation. A number of studies discussing the problem and some methods dealing with its solution are analyzed. Recursion and iteration are approaches used in computer programs to implement different algorithms. An iterative approach is the repeated execution of the same source code until a certain end condition is met. On the other hand, a recursive approach uses a recursive function that repeatedly calls itself. This function contains a source code that must be executed repeatedly. Both algorithms presented in this paper can be used to generate permutations of an n element set. The algorithms are modified so that they can be used to solve the Travelling Salesman Problem (TSP) with a small number of vertices. Several publications that discuss the TSP and some approaches to its solution are also presented. The methodology and the conditions for conducting the experiments are described in details. The obtained results have been analyzed; they show that for the same conditions the iterative algorithm works from of 8 to 16 times faster than the recursive algorithm in all the tested input data. Several approaches to optimize the two algorithms in terms of the number of permutations tested when searching a minimal Hamiltonian cycle are presented

An Evaluation of The Mobile Apps for Children with Special Education Needs Based on The Utility Function Metrics

Mobile apps can be used in various environments and at any time. People used them for learning, communications, and entertainment. Because of the ease use of mobile devices interface (like smartphone and tablet), then everyone, including the children with special needs, can have used them. In recent years, there has been an increase in the efforts of educational institutions and of scientists to support children in their daily life. Ongoing developments in communication and information technologies contribute to this process. The main goal of this study is to present the basic functional requirements for the mobile apps for children with special needs. The current state of the scientific research related to the design and development of mobile apps is discussed. This issue became very important in the last years because of an increase in the number of children with special needs on a worldwide scale is observed. And the same time the increase in the use of mobile technologies of them. The proposed model for the evaluation of potential utility provides for the classification of the mobile applications designed for children with special needs about their functionality features. This model is based on our studies of the state-of-art scientific works of many authors. Whit the model for the evaluation of potential utility, the 27 mobile applications for children with special needs, downloaded from the mobile application stores: Apple Store, Google Play and Store Windows Phone Apps, were classified and analyzed. The results showed that despite the variety of mobile applications, those that are suitable for children with special needs are too few. Most of the applications cover only half of the evaluation criteria, which means they have functionalities only for individual needs. Therefore, the proposed utility function metrics of the evaluation can be used as a basis for interface developing for mobile apps, appropriate for children with special needs

A comparative analysis between two heuristic algorithms for the graph vertex coloring problem

This study focuses on two heuristic algorithms for the graph vertex coloring problem: the sequential (greedy) coloring algorithm (SCA) and the Welsh–Powell algorithm (WPA). The code of the algorithms is presented and discussed. The methodology and conditions of the experiments are presented. The execution time of the algorithms was calculated as the average of four different starts of the algorithms for all analyzed graphs, taking into consideration the multitasking mode of the operating system. In the graphs with less than 600 vertices, in 90% of cases, both algorithms generated the same solutions. In only 10% of cases, the WPA algorithm generates better solutions. However, in the graphs with more than 1,000 vertices, in 35% of cases, the WPA algorithm generates better solutions. The results show that the difference in the execution time of the algorithms for all graphs is acceptable, but the quality of the solutions generated by the WPA algorithm in more than 20% of cases is better compared to the SC algorithm. The results also show that the quality of the solutions is not related to the number of iterations performed by the algorithms

An analysis between different algorithms for the graph vertex coloring problem

This research focuses on an analysis of different algorithms for the graph vertex coloring problem. Some approaches to solving the problem are discussed. Moreover, some studies for the problem and several methods for its solution are analyzed as well. An exact algorithm (using the backtracking method) is presented. The complexity analysis of the algorithm is discussed. Determining the average execution time of the exact algorithm is consistent with the multitasking mode of the operating system. This algorithm generates optimal solutions for all studied graphs. In addition, two heuristic algorithms for solving the graph vertex coloring problem are used as well. The results show that the exact algorithm can be used to solve the graph vertex coloring problem for small graphs with 30-35 vertices. For half of the graphs, all three algorithms have found the optimal solutions. The suboptimal solutions generated by the approximate algorithms are identical in terms of the number of colors needed to color the corresponding graphs. The results show that the linear increase in the number of vertices and edges of the analyzed graphs causes a linear increase in the number of colors needed to color these graphs