Journal of Algorithms and Computation
Volume:51 Issue: 1, Jun 2019

Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and important problems of computational geometry. In this paper a new algorithm is presented for computing the convex hull of a set of random points in the plane by using a sweep-line strategy. The sweep-line is a horizontal line that is moved from top to bottom on a map of points. Our algorithm is optimal and has time complexity $O(nlogn)$ where $n$ is the size of input.

Prediction of heart disease is very important because it is one of the causes of death around the world. Moreover, heart disease prediction in the early stage plays a main role in the treatment and recovery disease and reduces costs of diagnosis disease and side effects it. Machine learning algorithms are able to identify an effective pattern for diagnosis and treatment of the disease and identify effective factors in the disease. this paper is investigated a new hybrid algorithm of Whale Optimization and Dragonfly algorithm using a machine learning algorithm. the hybrid algorithm employs a Support Vector Machine algorithm for effective Prediction of heart disease. Proposed method is evaluated by Cleveland standard heart disease dataset. The experimental result indicates that the SVM accuracy of 88.89 $%$ and nine features are selected in this respect.

In many industrial and non-industrial applications, it is necessary to identify the largest inscribed rectangle in a certain shape. The problem is studied for convex and non-convex polygons. Another criterion is the direction of the rectangle: axis aligned or general. In this paper a heuristic algorithm is presented for finding the largest axis aligned inscribed rectangle in a general polygon. Comparing with stare of the art, the rectangles resulted from our algorithm have bigger area. We also proposed an approach to use the algorithm for finding a rectangle with general direction.

Optimization of inventory costs is the most important goal in industries. But in many models, the constraints are considered simple and relaxed. Some actual constraints are to consider the combinatorial production and purchase models in multi-products environment. The purpose of this article is to improve the efficiency of inventory management and find the economic order quantity and economic production quantity that can minimize the cost of inventory and customer satisfaction. In this study, the models with these targets in combinatorial production and purchase systems with the assumption the warehouse and budget constraints are proposed. Since a long time for solving the problem with an exact method is required, we develop a genetic algorithm. To evaluate the efficiency of the proposed algorithm, test problems with different sizes of the problem in the range from 1 to 2000 jobs, are generated. The results show that the genetic method is efficient to determine economic order quantity and economic production quantities. The computational results demonstrate that the average error of the solution is 10.93%.

Minimum and maximum operators are two well-known t-norm and s-norm used frequently in fuzzy systems. In this paper, two different types of fuzzy inequalities are simultaneously studied where the convex combination of minimum and maximum operators is applied as the fuzzy relational composition. Some basic properties and theoretical aspects of the problem are derived and four necessary and sufficient conditions are presented. Moreover, an algorithm is proposed to solve the problem and an example is described to illustrate the algorithm.

In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than solving the problem in each step using conventional iterative methods, a closed-form solution is formulated..

Here are many situations in real applications of decision making where we deal with uncertain conditions.  Due to the different sources of uncertainty,  since its original definition of fuzzy sets in 1965 cite{zadeh1965},  different generalizations and extensions of fuzzy sets have been introduced: Type-2 fuzzy sets cite{6,13}, Intuitionistic fuzzy sets cite{1}, fuzzy multi-sets cite{37} and etc. However, in such cases, it is suitable for experts to provide their preferences or assessments by using linguistic information rather than quantitative values.

The explicitly restarted Arnoldi method (ERAM) can be used to find some eigenvalues of large and sparse matrices. However, it has been shown that even this method may fail to converge. In this paper, we present two new methods to accelerate the convergence of ERAM algorithm. In these methods, we apply two strategies for the updated initial vector in each restart cycles. The implementation of the methods have been tested by numerical examples. The results show that we can obtain a good acceleration of the convergence compared to original ERAM.

We consider the problem of finding the localization of radioactive source by using data from a digital camera. In other words, the camera could help us to detect the direction of radioactive rays radiation. Therefore, the outcome could be used to command a robot to move toward the true direction to achieve the source. The process of camera data is performed by using image processing and computational geometry algorithms. And the robot is looking for the source in a space with geometrical obstacles. Lots of radioactive accidents daily occur all over the world. During the radiography, the radioactive source is sometimes thrown out from its protection layer and the radiographer has to look for it in the space around. This would have lots of irreparable costs. Thus, it seems necessary to make a robot which could search the radioactive source intelligently.

Let $G$ be a graph. Let $f:V(G)to{0,1,2, ldots, k-1}$ be a map where $k in mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $left|f(u)-f(v)right|$. $f$ is called a $k$-total difference cordial labeling of $G$ if $left|t_{df}(i)-t_{df}(j)right|leq 1$, $i,j in {0,1,2, ldots, k-1}$ where $t_{df}(x)$ denotes the total number of vertices and the edges labeled with $x$.A graph with admits a $k$-total difference cordial labeling is called a $k$-total difference cordial graphs. We investigate $k$-total difference cordial labeling of some graphs and study the $3$-total difference cordial labeling behaviour of star,bistar,complete bipartiate graph,comb,wheel,helm,armed crown etc.the formula is not displayed correctly!

A chord of a path $P$ is an edge joining two non-adjacent vertices of $P$. A path  $P$ is called a monophonic path if it is a chordless path. A longest $x-y$ monophonic path is called an $x-y$ detour monophonic path. A  detour monophonic graphoidal cover of a graph $G$ is a collection $psi_{dm}$ of detour monophonic paths in $G$ such that every vertex of $G$ is an internal vertex  of at most one  detour monophonic path in $psi_{dm}$ and every edge of $G$ is in exactly one  detour monophonic path in $psi_{dm}$. The minimum cardinality of a  detour monophonic graphoidal cover of $G$ is called the  detour monophonic graphoidal covering number of $G$ and is denoted by $eta_{dm}(G)$. In this paper, we find the  detour monophonic graphoidal covering number of corona product of wheel with some standard graphs

Reliability of networks is an important issue in the field of graph and network. Computation of network vulnerability parameters is NP-complete for popular network topologies such as tree, Mesh, Cube, etc.In this paper, we will show that the tenacity and rupture degree parameters for trapezoid graphs can be computed in polynomial time.