https://jac.ut.ac.ir/ Journal of Algorithms and Computation en daily 1 Thu, 13 Jan 2022 00:00:00 +0330 Thu, 13 Jan 2022 00:00:00 +0330 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. https://jac.ut.ac.ir/article_85483.html  A popular research topic in Graph Convolutional Networks (GCNs) is to speedup the training time of the network.  The main bottleneck in training GCN is the exponentially growing of computations. 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  overlapped clustering, instead of crisp clustering which is used in  Cluster-GCN.  This is achieved by allowing the marginal nodes to contribute to training in more than one cluster.  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. 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} ,& \text{if $p$ is even}\\\frac{p-1}{2} ,& \text{if $p$ is odd}\\\end{cases}\end{equation*}\\  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  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 $\left|\Delta_{f_1} - \Delta_{f_1^c}\right| \leq 1$,  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. 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. https://jac.ut.ac.ir/article_85486.html We introduce a new invariant vulnerability parameter named “J-Tightness” or “J(G)” 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. 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.  https://jac.ut.ac.ir/article_85488.html The statistical methods based on cumulative distribution function is a start point for  many parametric or nonparametric statistical inferences. However, there are many practical problems that require dealing with observations/parameters that represent inherently imprecise.  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  fuzzy cumulative distribution function. However, the main properties of the proposed method has not yet been considered in fuzzy environment.  This paper aims to extend  the classical properties of the fuzzy cumulative distribution function in fuzzy environment. 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. 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 $Vis(S,{\cal O})$  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  of the visibility graph $Vis(S,{\cal O})$ of  degree at most 6. Moreover, we show that there is a plane $1.88$-spanner of the visibility graph $Vis(S,{\cal O})$.  These  improve the stretch factor and the maximum degree  of the previous results by A. van Renssen and  G. Wong ({\em Theoretical Computer Science, 2021}) in the context of points in convex position. 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. 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. https://jac.ut.ac.ir/article_85501.html  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. 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.  This DEAR method serves as a user-friendly method in selecting the best journal. https://jac.ut.ac.ir/article_85517.html An edge  coloring of a digraph  $D$ is called a $P_3$-rainbow edge coloring if  the edges of any directed path of $D$ with length 2 are colored with different colors. It is proved that  for a $P_3$-rainbow edge coloring of  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\}$  colors are enough. One can determine in linear time if  a digraph has a  $P_3$-rainbow edge coloring with 1 or 2 colors. In this paper, it is proved that  determining   that a digraph has a  $P_3$-rainbow edge coloring  with 3 colors is an NP-complete problem even for planar digraphs. Moreover, it is shown that  $\left\lceil{log_2{\chi(D)}}\right\rceil$ colors is necessary and sufficient for a $P_3$-rainbow edge coloringof a transitive orientation digraph $D$.  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. https://jac.ut.ac.ir/article_106204.html Wireless Sensor Networks (WSNs) play a crucial role in monitoring and surveillance, yet random deployment often causes uneven coverage and redundant sensing. This study introduces a Chaos-Enhanced Superb Fairy-wren Optimization Algorithm (CE-SFOA), which integrates chaotic dynamics through a Cubic map into the position update and parameter control mechanisms. The chaotic modulation enhances population diversity, balances exploration and exploitation, and mitigates premature convergence. Experiments across three deployment scenarios show that CE-SFOA consistently achieves higher coverage and faster convergence than SFOA and seven competing metaheuristics, yielding 5.32–6.65% coverage improvement over the baseline. These findings demonstrate that chaotic modulation is an effective strategy for enhancing metaheuristic performance in WSN coverage optimization. https://jac.ut.ac.ir/article_106205.html Recent advances in federated learning and IoT-driven edge analytics underscore the need for optimization techniques that are both scalable and privacy-preserving[1][2]. In this work, we introduce ADMM-DP, a variant of the Alternating Direction Method of Multipliers that seamlessly integrates differential privacy (DP) guarantees in a fully decentralized, multi-agent learning architecture[3]. ADMM-DP leverages an augmented Lagrangian formulation with adaptive inexact local updates and calibrated Gaussian noise injection into each exchanged message, ensuring rigorous (ε,δ)-DP without sacrificing convergence[4][5]. Theoretically, we establish convergence rates and privacy-utility bounds under realistic heterogeneous (non-IID) data conditions. Building on DP-ADMM literature, we prove that ADMM-DP converges to a stationary solution with an explicit utility-privacy tradeoff[6], and furthermore, for strongly convex losses the method attains linear convergence rates comparable to non-private ADMM[7]. Privacy loss is tracked via advanced composition (moments accountant) to yield tight end-to-end DP guarantees[8]. https://jac.ut.ac.ir/article_106206.html The video game industry (VGI) faces significant challenges in today’s world. Game designers continually strive to create innovative scenarios that engage players and enhance their motivation to play. However, developing such scenarios is a complex task, and evaluating their difficulty during the design phase is equally challenging. In this paper, we focus on the Wumpus World game and propose a model for it using Coloured Petri Nets (CPNs). The proposed model enables designers to simulate various game scenarios and assess their difficulty levels without modifying the underlying structure by simply changing the tokens of the model. Since in most games, players need to switch between. Since, in most games, players must transition between different states to achieve their objectives, the mapping approach introduced here can also be applied to model and simulate other games. https://jac.ut.ac.ir/article_106207.html Ensuring equity in educational assessment is essential for providing equitable learning opportunities to all students, regardless of their gender, race, or socio-economic background. However, persistent disparities in large-scale educational evaluations indicate that data-driven models may unintentionally amplify existing inequities when trained on biased data. This study evaluates the effectiveness of two causal fairness–modification algorithms—MData and Matrix Factorization (MF)—in mitigating discrimination within the TIMSS student-achievement dataset. MData applies threshold-based causal label modifications, whereas MF reconstructs group-level distributions by enforcing conditional independence through factorization. Experimental results demonstrate that both algorithms substantially mitigate discrimination across gender, race, and socio-economic status. MData consistently preserves superior predictive accuracy, while MF achieves greater fairness gains under an appropriate configuration. Together, these findings underscore the potential of causal pre-processing techniques to modify biased datasets and enhance equity in educational analytics. They also highlight the importance of integrating fairness-aware data modification into large-scale assessment pipelines. https://jac.ut.ac.ir/article_106208.html This paper presents a numerical stochastic kinematic analysis of the velocity response of a six-degree-of-freedom PUMA560 robotic manipulator under white/colored noise. Stochastic disturbances are injected directly into the joint motion functions, and the resulting linear/angular velocities of the end effector are computed using the manipulator Jacobian. White noise is modeled as the derivative of Brownian motion, while colored noise is represented by Ornstein–Uhlenbeck processes. Numerical simulations are conducted using first-, third-, and fifth-order polynomial joint trajectories, and noise effects are quantitatively evaluated using the Root-Mean-Square-Error (RMSE). The results demonstrate that higher-order joint trajectories amplify noise-induced deviations in end-effector velocity. Comparative analysis shows that the manipulator exhibits greater robustness to colored noise than to white noise. Additionally, variations in link lengths indicate that linear velocity sensitivity increases with link length, whereas angular velocity remains largely unaffected. These findings provide insights for improving manipulator design and velocity accuracy under stochastic disturbances. https://jac.ut.ac.ir/article_106209.html Direct Current (DC) Electrical Resistivity Tomography (ERT) inversion is a non-linear, ill-posed problem requiring robust solvers for accurate subsurface resistivity reconstruction. This study systematically compares four second-order unconstrained iterative solvers which are Simple Newton, Newton-CG, Trust-Exact, and Trust-NCG, using synthetic dipole-dipole data with conductive and resistive anomalies in a homogeneous background. Inversion is performed within a finite-element framework with unstructured triangular meshes. Solver performance is assessed through reconstruction accuracy and computational efficiency using error metrics and data misfit. Results show Simple Newton fails due to instability and fixed step sizes. Newton-CG, Trust-Exact, and Trust-NCG converge reliably, with Trust-Exact and Trust-NCG markedly superior in resolving sharp resistivity contrasts, especially the conductive anomaly, owing to adaptive trust-region globalization. Newton-CG and Trust-NCG exhibit minor smoothing, reflecting a trade-off between speed and precision. These findings highlight the superiority of trust-region methods in weakly regularized non-linear geophysical inversion, emphasizing their ability to preserve sharp contrasts. https://jac.ut.ac.ir/article_106220.html With the emergence of Generative Flow Networks (GFlowNets) as a new paradigm in amortized inference, significant questions have arisen regarding the standing of traditional sampling methods such as Markov Chain Monte Carlo (MCMC). While generative models promise to mitigate ”mode mixing” challenges, their precise performance boundaries compared to computationally cheaper classical methods remain ambiguous. In this study, we conduct a comprehensive comparative evaluation between major GFlowNet objectives (including TB, DB, and FM) and the Metropolis-Hastings algorithm within discrete environments. The primary focusof this investigation is to analyze the sensitivity of these models to ”Reward Landscape Geometry” and dimensional complexity. We examine under which conditions the computational overhead of training a deep model is justifiable and identifying the critical points where traditional methods maintain their robustness. The findings of this research provide novel insights into selecting the optimal sampling strategy, regarding the universal su-periority of learning-based approaches. https://jac.ut.ac.ir/article_106211.html M =(1, 2, · · · , p2 , 12 , 13 , · · · , 2p+2, if p is even1, 2, · · · , p−12 , 12 , 13 , · · · , 2p+3, if p is oddLet χ : V (G) → M be a bijection.For each edge xy assignthe label ⌈χ(x)χ(y)⌉. χ is called a fractional productcordial labeling (simply called FP-cordial labeling)if |Πχ(0) − Πχ(1)| ≤ 1, where Πχ(1) and Πχ(0) respectivelydenotes the number of edges labelled with 1 andnot labelled with 1. A graph with a fractional productcordial labeling is called a fractional product cordialgraph (Simply FP-cordial graph).We investigatethe fractional product cordial labeling behaviourof lotus graph, necklace graph, hurdlegraph, key graph, coconut tree, prism, mobious ladder,vanessa graph and udukkai graph. https://jac.ut.ac.ir/article_106212.html The error function, erf(x), is crucial in many fields but lacks a closed-form solution. To improve existing closed-form approximations, this paper introduces a global-optimization framework that refines their numerical coefficients without changing their analytical form. The optimization minimizes a composite objective of mean and maximum absolute error (MAE and Max-AE) over selected domains. We solve this using the Gaussian Combined Arms (GCA) metaheuristic. For 16 structural types, the method often reduces error by an order of magnitude while maintaining formula simplicity and low cost. We also present new, highly accurate approximations with closed-form inverses. The framework is a powerful, transferable tool for enhancing approximations of erf(x) and related functions. https://jac.ut.ac.ir/article_106215.html Outdoor cameras play a vital role in security and social governance systems. However, bad weathercan significantly reduce image quality. This can hinder the effectiveness of these systems. This study proposes a new method to remove fog from images captured by outdoor cameras. Unlike traditional methods that analyze small square areas of the image, our approach works with superpixels, which are smarter groupings of pixels. The algorithm first calculates the ”dark channel” for each superpixel. The proposed method then merges superpixels with close dark channel values. To prevent unwanted halos around objects after removing the fog, the algorithm applies ”guided filtering” to the merged dark channel. The effectiveness of this new approach is compared to existing methods using varioustests that measure image quality. The results show that the proposed method outperforms existing algorithms. This allows for clearer images and improved performance of security and social governance systems. Details and numerical rsults might be seen at https://my.uupload.ir/dl/v9EnmnBr. https://jac.ut.ac.ir/article_106213.html Computing the convex hull of a set of points is a fundamental problem in computer science that has applications in various scientific and engineering domains. This paper presents a preprocessing algorithm, named Tiling, that can be utilized before any desired algorithm for computing the convex hull of a set of $n$ points randomly distributed in $\mathbb{R}^3$ by uniform distribution. The key contributions of this work are threefold. First, we provide a complete preprocessing algorithm with detailed implementation. Second, we present rigorous experimental validation showing $2-2.6\times$ performance improvements over the widely used Qhull implementation when applied to uniformly distributed point sets in space. Third, our algorithm demonstrates the ability to eliminate approximately $95-97\%$ of input points while maintaining convex hull correctness, significantly reducing the computational burden for subsequent hull computation. https://jac.ut.ac.ir/article_106214.html There are well-established Online Algorithms for the Static List Access problem. However, the competitive ratio of dynamic list updating needs more investigations. We have formalized the quantitative analysis of several dynamic classical algorithms, such as MTF, RMTF, BIT, and TIMESTAMP. In MTF, we used the factorization lemma and proved that 3n/2 holds for the two-element state, and then we could extend it to the general state, and the result was 2 − 2 /(l+1) . We showed that RMTFp has a lower bound ε−p for p∈(0,1). In the dynamic BIT algorithm, we propose a lower bound for the expectation of its competitive ratio for update operations. We proved that the TIMESTAMP algorithm is 2-competitive by analyzing the costs of inserting, deleting, and accessing request sequences. 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–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's method. https://jac.ut.ac.ir/article_106551.html Traditional Computational Fluid Dynamics (CFD) methods demand significant computational resources. Graph Network-based Simulators (GNS) have emerged as powerful surrogates, modeling complex physical systems by learning spatial-temporal interactions. In this paper, we evaluate a GNS model on nine exact analytical solutions of the Navier-Stokes equations, comprising four 2D and five 3D flows. By training the network to predict fluid particle evolution using localized message passing, we bypass Eulerian grid constraints and simulate fluid topologies in a Lagrangian framework. Our results demonstrate that the GNS approach achieves highly accurate rollouts (MSE $< 0.01$) while successfully capturing complex structures like viscous vortex decay. The model achieves its lowest rollout Mean Total MSE of $3.7852 \times 10^{-3}$ on the Lamb-Oseen 2D model, highlighting the generalizability and precision of deep graph architectures for exact fluid mechanics phenomena.