In a graph proposition, an Eulerian trail refers to a graph that moves to each edge precisely once. On the same note, Eulerian circuits (Eulerian cycle) refers to Eulerian trail that originates and stops on the one vertex. This was first applied by Leonard Euler whereby he stated that appropriate condition for the presence of Eulerian circuits is that the entire graph vertices have even level, and illustrated without confirming that joined graphs with having even degree entails Eulerian circuit. Euler tour within an undirected graph refers to a cycle, which applies every edge just once. When such a cycle is present, the graph is referred to as unicursal. Whereas graphs of that nature are Eulerian graphs, it is advisable to note that not each Eulerian graph comprises of an Eulerian circuit (Goodrich & Tamassia, 2006).
Nearest neighbor is a type or method of process, certainly in orderly and frequent approach of attaining something. Usually, it implies systematic arrangement of sections or procedure of ending something or random attempts, which lack an approach. In practice, an essential evaluation way of addressing huge volume of data is the nearest neighbor (NN) problem (Goodrich & Tamassia, 2006). For NN problem, the purpose is to prearrange a set of objects that they will afterwards be given a query object; a person may find successfully the information object equivalent to the query. This issue entails a wide set of usage in data analysis and organization. For example, it generates the source of extensively applied category approach in machine learning. To illustrate the objects and the similarity standards, a person usually applies geometric concepts. For instance, a high-dimensional vector, having a single coordinate per pixel, while the equivalence standard measure can be the measure of illustrating objects through high dimensional element vectors, can shape a black-and-white figure (Goodrich & Tamassia, 2006).
The sorted edges algorithm
The sorted edges algorithm is a form of algorithm, which consists of the edges ranging from the smallest to the largest. It often considers the order of the edges, ranging from the smallest to the largest and gives the mathematician a choice to choose the use of the Hamiltonian algorithm. The main characteristics of the sorted edge algorithm are that it does not bring together two edges to meet at a central point and it does not close a given circuit, which has been formed unless it is on an Hamiltonian algorithm (Cormen, 2001).
Kruskal’a algorithm is a type of algorithm, which utilizes the graph method in determining ht minimum weight, which is connected to a graph. This implies that it unearths a subset of the edges that constitutes the vertex of a tree, where the weight expected is made low. Greedy algorithm forms the main branch of the Kruskal’a algorithm. In this form of algorithm, every step, which is taken into consideration, is that with the least cost implying that it still falls under the greedy policy. The side, which brings together the needs of one single tree, is often rejected and not looked into because it could develop a circle , which may be harmful to the tree itself (Cormen, 2001).
Characteristics of the simplex method
There are several characteristics, which are attributed to the simplex method as a form of linear programming. One is that in this method, it utilizes the iterative process when the computations are being done. This means that repetition of the subjects under consideration is done, while following a given manner. The repetitive process is done so as to be able to obtain an optimal result. The second characteristic is that this process involves generation of the best solutions by following a given systematic process (Rudin, 1998).
The simplex method is also characterized by the generation of a largest solution than the initial one, when compared to the objective function. This element is important in the simplex method, since it enables the learner to be able to generate a clue toward the actual answer.
In the end, through this process, the optimum solution will be obtained. The simplex method is also characterized as the process, which tries to generate solutions to problems, which involves more than two variables (Rudin, 1998). Through the process of arriving to the answer is a long and lengthy process, another characteristics of the simplex method is that involves the simples mathematical operations like addition, multiplication, subtraction and division. Because of this, students are normally advised to be very keen while performing these operations and must therefore have knowledge in this areas before hand.
Cormen, T., Leiserson,C., Rivest, R. and Stein, C. (2001). Introduction to Algorithms,
Second Edition. New York, NY: MIT Press and McGraw-Hill
Goodrich, M. and Tamassia, R. (2006). Data Structures and Algorithms in Java, Fourth
Edition. New York, NY: John Wiley & Sons
Rudin, W. (1998). Principles of Mathematical Analysis (Third Edition). New York, NY: