Journal of Algorithms and Computation
https://jac.ut.ac.ir/
Journal of Algorithms and Computationendaily1Thu, 01 Jun 2023 00:00:00 +0430Thu, 01 Jun 2023 00:00:00 +0430$4$-total mean cordial labeling of spider graph
https://jac.ut.ac.ir/article_92447.html
Let $G$ be a graph. Let $f:V\left(G\right)\rightarrow \left\{0,1,2,\ldots,k-1\right\}$ be a function where $k\in \mathbb{N}$ and $k&gt;1$. For each edge $uv$, assign the label $f\left(uv\right)=\left\lceil \frac{f\left(u\right)+f\left(v\right)}{2}\right\rceil$. $f$ is called a $k$-total mean cordial labeling of $G$ if $\left|t_{mf}\left(i\right)-t_{mf}\left(j\right) \right| \leq 1$, for all $i,j\in\left\{0,1,2,\ldots,k-1\right\}$, where $t_{mf}\left(x\right)$ denotes the total number of vertices and edges labelled with $x$, $x\in\left\{0,1,2,\ldots,k-1\right\}$. A graph with admit a $k$-total mean cordial labeling is called $k$-total mean cordial graph. In this paper we investigate the $4$-total mean cordial labeling behaviour of some spider graph.A variant of van Hoeij's algorithm to compute hypergeometric term solutions of holonomic recurrence equations
https://jac.ut.ac.ir/article_85482.html
Linear and homogeneous recurrence equations having polynomial coefficients are said to be holonomic. These equations are useful for proving and discovering combinatorial and hypergeometric identities. Given a field $\mathbb{K}$ of characteristic zero, $a_n$ is a hypergeometric term with respect to $\mathbb{K}$, if the ratio $a_{n+1}/a_n$ is a rational function over $\mathbb{K}$. Two algorithms by Marko Petkov\v{s}ek (1993) and Mark van Hoeij (1999) were proposed to compute hypergeometric term solutions of holonomic recurrence equations. The latter algorithm is more efficient and was implemented by its author in the Computer Algebra System (CAS) Maple through the command \texttt{LREtools[hypergeomsols]}.
We describe a variant of van Hoeij's algorithm that performs with the same efficiency without considering certain recommendations of the original version. We implemented our algorithm in the CASes Maxima and Maple. It also appears for some particular cases that our code finds results where \texttt{LREtools[hypergeomsols]} fails.Overlapping Clusters in Cluster Convolutional Networks
https://jac.ut.ac.ir/article_85483.html
&nbsp;A popular research topic in Graph Convolutional Networks (GCNs) is to speedup the training time of the network.&nbsp;&nbsp;The main bottleneck in training GCN is the exponentially growing of computations.&nbsp;In Cluster-GCN based on this fact that each node and its neighbors are usually grouped in the same cluster, considers the clustering structure of the graph, and expand each node's neighborhood within each cluster when training GCN.The main assumption of Cluster-GCN is the weak relation between clusters; which is not correct at all graphs. Here we extend their approach by &nbsp;overlapped clustering, instead of crisp clustering which is used in &nbsp;Cluster-GCN. &nbsp;This is achieved by allowing the marginal nodes to contribute to training in more than one cluster. &nbsp;The evaluation of the proposed method is investigated through the experiments on several benchmark datasets.The experimental results show that the proposed method is more efficient than Cluster-GCN, in average.Pair difference cordial labeling of planar grid and mongolian tent
https://jac.ut.ac.ir/article_85484.html
\noindent Let $G = (V, E)$ be a $(p,q)$ graph.\\Define \begin{equation*}\rho =\begin{cases}\frac{p}{2} ,&amp; \text{if $p$ is even}\\\frac{p-1}{2} ,&amp; \text{if $p$ is odd}\\\end{cases}\end{equation*}\\&nbsp;&nbsp;and $L = \{\pm1 ,\pm2, \pm3 , \cdots ,\pm\rho\}$ called the set of labels.\\\noindent Consider a mapping $f : V \longrightarrow L$ by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when $p$ is odd.The labeling as defined &nbsp;above is said to be a pair difference cordial labeling if for each edge $uv$ of $G$ there exists a labeling $\left|f(u) - f(v)\right|$ such that $\left|\Delta_{f_1} - \Delta_{f_1^c}\right| \leq 1$, &nbsp;where $\Delta_{f_1}$ and $\Delta_{f_1^c}$ respectively denote the number of edges labeled with $1$ and number of edges not labeled with $1$. A graph $G$ for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate pair difference cordial labeling behavior of planar grid and mangolian tent graphs.A comparison between the resolution and linear optimization of FREs defined by product t-norm and geometric mean operator
https://jac.ut.ac.ir/article_85485.html
In this paper, a type of fuzzy system is firstly investigated whereby the feasible region is defined by the fuzzy relational equalities and the geometric mean as fuzzy composition. Some related basic and theoretical properties are derived and the feasible region is completely determined. Moreover, a comparison is made between this region and FRE defined by product t-norm. Finally, an example is described to illustrate the differences of these two FRE systems.On the J-Tightness of Graphs
https://jac.ut.ac.ir/article_85486.html
We introduce a new invariant vulnerability parameter named &ldquo;J-Tightness&rdquo; or &ldquo;J(G)&rdquo; for graphs. As a stability measure, its properties along with comparisons to other parameters of a graph are proposed. We show how it is calculated for complete graphs and cycles. We show that J-Tightness better fits the properties of vulnerability measures and can be used with more confidence to assess the vulnerability of any classes of graphs.A fast algorithm for the linear programming problem constrained with the Weighted power mean -- Fuzzy Relational Equalities (WPM-FRE)
https://jac.ut.ac.ir/article_85487.html
In this paper, a linear programming problem is investigated in which the feasible region is formed as a special type of fuzzy relational equalities (FRE). In this type of FRE, fuzzy composition is considered as the weighted power mean operator (WPM). Some theoretical properties of the feasible region are derived and some necessary and sufficient conditions are also presented to determine the feasibility of the problem. Moreover, two procedures are proposed for simplifying the problem. Based on some structural properties of the problem, an algorithm is presented to find the optimal solutions and finally, an example is described to illustrate the algorithm.&nbsp;Fuzzy Cumulative Distribution Function \and its Properties
https://jac.ut.ac.ir/article_85488.html
The statistical methods based on cumulative distribution function is a start point for &nbsp;many parametric or nonparametric statistical inferences. However, there are many practical problems that require dealing with observations/parameters that represent inherently imprecise. &nbsp;However, Hesamian and Taheri (2013) was extended a concept of fuzzy cumulative distribution function. Applying a common notion of fuzzy random variables, they extended a vague concept of &nbsp;fuzzy cumulative distribution function. However, the main properties of the proposed method has not yet been considered in fuzzy environment. &nbsp;This paper aims to extend &nbsp;the classical properties of the fuzzy cumulative distribution function in fuzzy environment.An algorithm to Solve the Linear Programming Problem Constrained with the Harmonicâ€“Fuzzy Relational Equalities
https://jac.ut.ac.ir/article_85497.html
In this paper, a linear programming problem is investigated in which the feasible region is formed as the intersection of fuzzy relational equalities and the harmonic mean operator is considered as fuzzy composition. Theoretical properties of the feasible region are derived. It is proved that the feasible solution set is comprised of one maximum solution and a finite number of minimal solutions. Furthermore, some necessary and sufficient conditions are additionally presented to determine the feasibility of the problem. Moreover, an algorithm is presented to find the optimal solutions of the problem and finally, an example is described to illustrate the algorithm.Plane Bounded-Degree Spanners Among the Obstacles for the Points in Convex Position
https://jac.ut.ac.ir/article_85498.html
Let $S$ be a set of points in the plane that are in convex position. Let~$\cal O$ be a set of simple polygonal obstacles whose vertices are in $S$. The visibility graph $Vis(S,{\cal O})$ &nbsp;is the graph which is obtained from the complete graph of $S$ by removing all edges intersecting some obstacle of $\cal O$. In this paper, we show that there is a plane $5.19$-spanner &nbsp;of the visibility graph $Vis(S,{\cal O})$ of &nbsp;degree at most 6. Moreover, we show that there is a plane $1.88$-spanner of the visibility graph $Vis(S,{\cal O})$. &nbsp;These &nbsp;improve the stretch factor and the maximum degree &nbsp;of the previous results by A. van Renssen and &nbsp;G. Wong ({\em Theoretical Computer Science, 2021}) in the context of points in convex position.Effective Tamper Detection and Recovery of Images after Serious Attacks
https://jac.ut.ac.ir/article_85499.html
Confirming the integrity of transmitted sensitive digital content is a significant issue due to the evolution in communication technologies and the accessibility of image processing tools. Watermarking has been a successful method of authentication and integrity verification recently. However, several significant problems remain such as confronting some serious attacks and recovery after higher tampering rates. We propose a hybrid method to enable an image to be recovered successfully after a range of attacks. A blind watermarking approach is adopted which includes fragile authentication but robust recovery references. This is performed by embedding verification code as part of the watermarked data along with key features of the original image into a location that is resistant to the attack. To combat different kinds of attacks, the areas of the image have been investigated to find which area is more likely to be affected in each type of specific attack.On the resolution of LP-FRE defined by the convex combination operator
https://jac.ut.ac.ir/article_85500.html
In this paper, a linear programming problem is investigated in which the feasible region is formed as a special type of fuzzy relational equalities (FRE). In this type of FRE, fuzzy composition is considered as the convex combination operator. It is proved that the feasible region of the problem can be written by one maximum solution and a finite number of minimal solutions. Some theoretical properties of the feasible region are derived and some necessary and sufficient conditions are also presented to determine the feasibility of the problem. Based on some structural properties of the problem, an algorithm is presented to find the optimal solutions and finally, an example is described to illustrate the algorithm.Priority-Oriented Task Scheduling based on Harris Hawks Optimizer for Cloud Computing
https://jac.ut.ac.ir/article_85501.html
&nbsp;Cloud computing is a high-performance computing environment that can remotely provide services to customers using a pay-per-use model. The principal challenge in cloud computing is task scheduling, in which tasks must be effectively allocated to resources. The mapping of cloud resources to customer requests (tasks) is a popular Nondeterministic Polynomial-time (NP)-Complete problem. Although the task scheduling problem is a multi-objective optimization problem, most task scheduling algorithms cannot provide an effective trade-off between makespan, resource utilization, and energy consumption. Therefore, this study introduces a Priority-based task scheduling algorithm using Harris Hawks Optimizer (HHO) which is entitled as PHHO. The proposed algorithm first prioritizes tasks using a hierarchical process based on length and memory. Then, the HHO algorithm is used for optimally assigning tasks to resources. The PHHO algorithm aims to decrease makespan and energy consumption while increasing resource utilization and throughput. To evaluate the effectiveness of the PHHO algorithm, it is compared with other well-known meta-heuristic algorithms such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Whale Optimization Algorithm (WOA), Salp Swarm Algorithm (SSA), and Moth-Flame Optimization (MFO). The experimental results show the effectiveness of the PHHO algorithm compared to other algorithms in terms of makespan, resource utilization, throughput, and energy consumption.A Systematic Way for Selecting Suitable Journal for Publishing Manuscripts
https://jac.ut.ac.ir/article_85516.html
\noindent Selecting suitable journals for publishing manuscripts for publication is one of the most essential processes before publishing any manuscript. Finding the relevant journal is a key factor which proves one's work valuable to the entire society. The final output and the performance of one's research is ultimately validated only if the paper is published in a right journal. One of the greatest mistakes that the authors make is submitting their manuscript in an unsuitable journal. The author should also consider all the six parameters such as Scope, Cite Score, Impact factor, Acceptance Rate, Time to first decision and Time to publication. Some authors only consider the acceptance rate and the time to first decision and publication as their main criteria. The author should consider all these parameters while publishing the paper. An algorithm named DEAR is used in the work which can consider all these parameters to find the right journal among the various alternatives. &nbsp;This DEAR method serves as a user-friendly method in selecting the best journal.$P_3$-Rainbow Edge Colouring of Digraphs
https://jac.ut.ac.ir/article_85517.html
An edge &nbsp;coloring of a digraph &nbsp;$D$ is called a $P_3$-rainbow edge coloring if &nbsp;the edges of any directed path of $D$ with length 2 are colored with different colors. It is proved that &nbsp;for a $P_3$-rainbow edge coloring of &nbsp;a digraph $D$, at least $\left\lceil{log_2{\chi(D)}} \right\rceil$ colors are necessary and $ 2\left\lceil{log_2{\chi(D)}}\right\rceil\}$ &nbsp;colors are enough. One can determine in linear time if &nbsp;a digraph has a &nbsp;$P_3$-rainbow edge coloring with 1 or 2 colors. In this paper, it is proved that &nbsp;determining &nbsp; that a digraph has a &nbsp;$P_3$-rainbow edge coloring &nbsp;with 3 colors is an NP-complete problem even for planar digraphs. Moreover, it is shown that &nbsp;$\left\lceil{log_2{\chi(D)}}\right\rceil$ colors is necessary and sufficient for a $P_3$-rainbow edge coloringof a transitive orientation digraph $D$.&nbsp;Negative Cost Girth Problem using Map-Reduce Framework
https://jac.ut.ac.ir/article_85518.html
On a graph with a negative cost cycle, the shortest path is undefined, but the number of edges of the shortest negative cost cycle could be computed. It is called Negative Cost Girth (NCG). The NCG problem is applied in many optimization issues such as scheduling and model verification. The existing polynomial algorithms suffer from high computation and memory consumption. In this paper, a powerful Map-Reduce framework implemented to find the NCG of a graph. The proposed algorithm runs in $O(\log_{}{k})$ parallel time over $O(n^3)$ on each Hadoop nodes, where $n, k$ are the size of the graph and the value of NCG, respectively. The Hadoop implementation of the algorithm shows that the total execution time is reduced by 50\% compared with polynomial algorithms, especially in large networks concerning increasing the numbers of Hadoop nodes. The result proves the efficiency of the approach for solving the NCG problem to process big data in a parallel and distributed way.Perfectionism Search Algorithm (PSA): An Efficient Meta-Heuristic Optimization Approach
https://jac.ut.ac.ir/article_92492.html
This paper proposes a novel population-based meta-heuristic optimization algorithm, called Perfectionism SearchAlgorithm (PSA), which is based on the psychological aspects of perfectionism. The PSA algorithm takes inspiration from one of the most popular model of perfectionism, which was proposed by Hewitt and Flett. During each iteration of the PSA algorithm, new solutions are generated by mimicking different types and aspects of perfectionistic behavior. In order to have a complete perspective on the performance of PSA, the proposed algorithm is tested with various nonlinear optimization problems, through selection of 35 benchmark functions from the literature. The generated solutions for these problems, were also compared with 11 well-known meta-heuristics which had been applied to many complex andpractical engineering optimization problems. The obtained results confirm the high performance of the proposedalgorithm in comparison to the other well-known algorithms.&nbsp;A new meta-heuristic algorithm of giant trevally for solving engineering problems
https://jac.ut.ac.ir/article_92495.html
As science and technology is progressing in engineering problems are also getting much more complex. So, solving these problems is of pivotal concern. Besides, the optimal solution among the solutions is of great value.
Among them, innovative algorithms inspired by artificial intelligence or the hunting behavior of animals in nature have a special place. In this article, a new algorithm named Giant Trevally Optimizer (GTO) is presented, by simulating the hunting strategy of this type of fish, a novel algorithm with the same title is introduced, which has been examined, and subjected to various tests and criteria. In the performance studies of the GTO algorithm with several efficient meta-heuristic algorithms to find the global optimal solution, fifteen criterion functions having various features along with two hard problems in engineering design were used. The performance of the GTO algorithm has been better than other algorithms.
&nbsp;On some main parameters of stochastic processes on directed graphs
https://jac.ut.ac.ir/article_92512.html
A random walk is a special kind of stochastic process of the Markov chain type. Some stochastic processes can be represented as a random walk on a graph. In this paper, the main parameters for a random walk on graph are examined.Pair Difference Cordial Labeling of Double Alternate Snake Graphs
https://jac.ut.ac.ir/article_92513.html
In this paper we investigate the pair difference cordial labeling behavior of double alternate triangular snake and double alternate quadrilatral snake graphs.An iterative method and maximal solution of Coupled algebraic Riccati equations
https://jac.ut.ac.ir/article_88681.html
Coupled Riccati equation has widely been applied to various engineering areas such as jump linear quadratic problem, particle transport theory, and Wiener&ndash;Hopf decomposition of Markov chains. In this paper, we consider an iterative method for computing Hermitian solution of the Coupled Algebraic Riccati Equations (CARE) which is usually encountered in control theory. We show some properties of this iterative method. Furthermore, it will also be demonstrated that the maximal solution can be obtained numerically via a certain linear or quadratic inequalities optimization problem. Numerical examples are presented and the results are compared.
Coupled algebraic Riccati equations; Maximal solution; Positive semidefinite matrix; Remodified Newton&#039;s method.