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Journal articles on the topic 'PageRank method'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Bu, Yi-Ming, and Ting-Zhu Huang. "An Adaptive Reordered Method for Computing PageRank." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/507915.

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We propose an adaptive reordered method to deal with the PageRank problem. It has been shown that one can reorder the hyperlink matrix of PageRank problem to calculate a reduced system and get the full PageRank vector through forward substitutions. This method can provide a speedup for calculating the PageRank vector. We observe that in the existing reordered method, the cost of the recursively reordering procedure could offset the computational reduction brought by minimizing the dimension of linear system. With this observation, we introduce an adaptive reordered method to accelerate the tot

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Shen, Zhao-Li, Yu-Tong Liu, Bruno Carpentieri, Chun Wen, and Jian-Jun Wang. "Recursive reordering and elimination method for efficient computation of PageRank problems." AIMS Mathematics 8, no. 10 (2023): 25104–30. http://dx.doi.org/10.3934/math.20231282.

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<abstract><p>The PageRank model is widely utilized for analyzing a variety of scientific issues beyond its original application in modeling web search engines. In recent years, considerable research effort has focused on developing high-performance iterative methods to solve this model, particularly when the dimension is exceedingly large. However, due to the ever-increasing extent and size of data networks in various applications, the computational requirements of the PageRank model continue to grow. This has led to the development of new techniques that aim to reduce the computat

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GLEICH, D. F., and K. KLOSTER. "Seeded PageRank solution paths." European Journal of Applied Mathematics 27, no. 6 (2016): 812–45. http://dx.doi.org/10.1017/s0956792516000280.

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We study the behaviour of network diffusions based on the PageRank random walk from a set of seed nodes. These diffusions are known to reveal small, localized clusters (or communities), and also large macro-scale clusters by varying a parameter that has a dual-interpretation as an accuracy bound and as a regularization level. We propose a new method that quickly approximates the result of the diffusion for all values of this parameter. Our method efficiently generates an approximatesolution pathorregularization pathassociated with a PageRank diffusion, and it reveals cluster structures at mult

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Pu, Bing-Yuan, Ting-Zhu Huang, Chun Wen, and Yi-Qin Lin. "The Extrapolation-Accelerated Multilevel Aggregation Method in PageRank Computation." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/525313.

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An accelerated multilevel aggregation method is presented for calculating the stationary probability vector of an irreducible stochastic matrix in PageRank computation, where the vector extrapolation method is its accelerator. We show how to periodically combine the extrapolation method together with the multilevel aggregation method on the finest level for speeding up the PageRank computation. Detailed numerical results are given to illustrate the behavior of this method, and comparisons with the typical methods are also made.

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Shen, Zhao-Li, Hao Yang, Bruno Carpentieri, Xian-Ming Gu, and Chun Wen. "A Preconditioned Variant of the Refined Arnoldi Method for Computing PageRank Eigenvectors." Symmetry 13, no. 8 (2021): 1327. http://dx.doi.org/10.3390/sym13081327.

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The PageRank model computes the stationary distribution of a Markov random walk on the linking structure of a network, and it uses the values within to represent the importance or centrality of each node. This model is first proposed by Google for ranking web pages, then it is widely applied as a centrality measure for networks arising in various fields such as in chemistry, bioinformatics, neuroscience and social networks. For example, it can measure the node centralities of the gene-gene annotation network to evaluate the relevance of each gene with a certain disease. The networks in some fi

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Vlasyuk, Vladislav, Oleg Galchonkov, and Alexander Nevrev. "An algebraic method for calculating PageRank." Eastern-European Journal of Enterprise Technologies 3, no. 2 (93) (2018): 6–12. http://dx.doi.org/10.15587/1729-4061.2018.131275.

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Yao, Yuhang, Xiao Zeng, Tianyue Cao, Luoyi Fu, and Xinbing Wang. "APRP: An Anonymous Propagation Method in Bitcoin Network." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 10073–74. http://dx.doi.org/10.1609/aaai.v33i01.330110073.

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Due to little attention given to anonymous protection against eavesdropping attacks in Bitcoin network, this paper initiatively proposes a solution to Bitcoin anonymization based on network structure. We first present a general adversarial network model for formulizing deanonymization attack, then present a novel propagation method APRP(Adaptive PageRank Propagation) that adopts PageRank as propagation delay factor and constantly adjusts PR-value of nodes to adapt to network dynamics. Experiments on both simulated and real Bitcoin networks confirm the superiority of APRP in terms of 20-50% per

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Feng, Yuehua, Yongxin Dong, and Jianxin You. "A Note on a Minimal Irreducible Adjustment Pagerank." Symmetry 14, no. 8 (2022): 1640. http://dx.doi.org/10.3390/sym14081640.

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The stochastic modification and irreducible modification in PageRank produce large web link changes correspondingly. To get a minimal irreducible web link adjustment, a PageRank model of minimal irreducible adjustment and its lumping method are discussed by Li, Chen, and Song. In this paper, we provide alternative proofs for the minimal irreducible PageRank by a new type of similarity transformation matrices. To further provide theorems and fast algorithms on a reduced matrix, an 4×4 block matrix partition case of the minimal irreducible PageRank model is utilized and analyzed. For some real a

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Zhang, He Ping, Ya Ping Zhao, and Ya Li Zhao. "Research on PageRank Algorithm to Index Pages." Applied Mechanics and Materials 198-199 (September 2012): 1469–74. http://dx.doi.org/10.4028/www.scientific.net/amm.198-199.1469.

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PageRank algorithm is a vital method to determine the importance of pages. Useful as it is, the algorithm has many disadvantages. Therefore, we arrive at the conclusion that it’s not rational to calculate the importance degree of pages simply by links between them. Considering the timeliness problem of PageRank algorithm, we provide the time penalty factor W(n) to weigh the effects of update time on page ranking. After adding the time penalty factor to the original PageRank algorithm, we come up with the refined PageRank algorithm. Our algorithm is superior compared with the original one and m

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Matthews, Nicole R., Andrew McClain, Chase M. L. Smith, and Adam G. Tennant. "Application of PageRank Algorithm to Division I NCAA men’s basketball as bracket formation and outcome predictive utility." Journal of Sports Analytics 7, no. 1 (2021): 1–9. http://dx.doi.org/10.3233/jsa-200425.

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This article examines the use of the PageRank algorithm to rank the teams and predict team performance in the tournament. This method has the potential to be utilized as an alternative method to choose tournament participants, as opposed to the traditional ranking and seeding process currently employed by the NCAA. PageRank allows for the consideration of all games played during the regular season (average of 5832 games per season) and for customizable performance weights in the prediction. The PageRank algorithm is a viable tool in predicting tournament outcomes due to depth and extensiveness

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Guo, Pei-Chang, Shi-Chen Gao, and Xiao-Xia Guo. "A Modified Newton Method for Multilinear PageRank." Taiwanese Journal of Mathematics 22, no. 5 (2018): 1161–71. http://dx.doi.org/10.11650/tjm/180303.

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12

Tan, Xueyuan. "A new extrapolation method for PageRank computations." Journal of Computational and Applied Mathematics 313 (March 2017): 383–92. http://dx.doi.org/10.1016/j.cam.2016.08.034.

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Namita, Namita, Sandeep Gupta, Arun Pratap Srivastava, Shashank Awasthi, and Krishan Saraswat. "Proficient Pivot Less Ongoing Individualized PageRanking." International Journal of Engineering & Technology 7, no. 4.39 (2018): 921–26. http://dx.doi.org/10.14419/ijet.v7i4.39.27729.

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In the period of enormous information, diminished models equipped for lessening huge information chart to appraise individualized PageRank are constrained. Individualized PageRank is a page rank estimation where irregular bounces are just permitted to a subdivision of begins pivots. The assets of ongoing procedure of figuring of individualized PageRank are exceedingly restrictive; hence we introduce a unique quick exact and fewer asset serious calculation for individualized PageRank issue. Quick Individualized PageRank finds objective pivot group. By using the reference to target group, the ca

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Migallón, Héctor, Violeta Migallón, and José Penadés. "Non-Stationary Acceleration Strategies for PageRank Computing." Mathematics 7, no. 10 (2019): 911. http://dx.doi.org/10.3390/math7100911.

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In this work, a non-stationary technique based on the Power method for accelerating the parallel computation of the PageRank vector is proposed and its theoretical convergence analyzed. This iterative non-stationary model, which uses the eigenvector formulation of the PageRank problem, reduces the needed computations for obtaining the PageRank vector by eliminating synchronization points among processes, in such a way that, at each iteration of the Power method, the block of iterate vector assigned to each process can be locally updated more than once, before performing a global synchronizatio

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Xie, Yajun, Lihua Hu, and Changfeng Ma. "A Parameterized Multi-Splitting Iterative Method for Solving the PageRank Problem." Mathematics 11, no. 15 (2023): 3320. http://dx.doi.org/10.3390/math11153320.

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In this paper, a new multi-parameter iterative algorithm is proposed to address the PageRank problem based on the multi-splitting iteration method. The proposed method solves two linear subsystems at each iteration by splitting the coefficient matrix, considering therefore inner and outer iteration to find the approximate solutions of these linear subsystems. It can be shown that the iterative sequence generated by the multi-parameter iterative algorithm finally converges to the PageRank vector when the parameters satisfy certain conditions. Numerical experiments show that the proposed algorit

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Tang, Shuting, Xiuqin Deng, and Rui Zhan. "The general tensor regular splitting iterative method for multilinear PageRank problem." AIMS Mathematics 9, no. 1 (2023): 1443–71. http://dx.doi.org/10.3934/math.2024071.

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<abstract><p>The paper presents an iterative scheme called the general tensor regular splitting iterative (GTRS) method for solving the multilinear PageRank problem, which is based on a (weak) regular splitting technique and further accelerates the iterative process by introducing a parameter. The method yields familiar iterative schemes through the use of specific splitting strategies, including fixed-point, inner-outer, Jacobi, Gauss-Seidel and successive overrelaxation methods. The paper analyzes the convergence of these solvers in detail. Numerical results are provided to demon

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Jin, Yu, Chun Wen, and Zhao-Li Shen. "Acceleration of the generalized FOM algorithm for computing PageRank." Electronic Research Archive 30, no. 2 (2022): 732–54. http://dx.doi.org/10.3934/era.2022039.

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<abstract><p>In this paper, a generalized full orthogonalization method (GFOM) based on weighted inner products is discussed for computing PageRank. In order to improve convergence performance, the GFOM algorithm is accelerated by two cheap methods respectively, one is the power method and the other is the extrapolation method based on Ritz values. Such that two new algorithms called GFOM-Power and GFOM-Extrapolation are proposed for computing PageRank. Their implementations and convergence analyses are studied in detail. Numerical experiments are used to show the efficiency of our

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Chen, Yang, Yepeng Qiu, and Wei Ren. "A normalized score-based weighted PageRank algorithm on ranking prediction of basketball games." Modern Physics Letters B 35, no. 18 (2021): 2150302. http://dx.doi.org/10.1142/s0217984921503024.

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Ranking of sports teams has always been significant to sponsors, coaches, as well as audiences. Prevailing prediction methods investigate probabilities by taking into account of different kinds of attributes (e.g. field goals, fields goal attempts) in order to establish a detail-based mechanism for analyzing the capability among competing teams. The different types of activation and inhibition actions between athletes provide a considerable challenge in the framework of network analysis. Moreover, these attributes interactions might add up the substantial redundancy to network frame as well. T

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Hsu, Yu-Chia, and Wen-Jie Zhang. "Applying PageRank to Team Ranking in Single-Elimination Tournaments: Evidence from Taiwan’s High School Baseball." Applied Sciences 15, no. 12 (2025): 6882. https://doi.org/10.3390/app15126882.

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This study examines the applicability of the well-established PageRank algorithm for ranking teams and predicting outcomes in incomplete, single-elimination high school baseball tournaments. Using match data from Taiwan’s CTBC Black Panther Cup National High School Baseball Tournament spanning from 2013 to 2023, this research investigates whether PageRank can produce valid, stable, and predictive rankings under structural constraints and limited data environments. Three empirical evaluations were conducted. First, a comparative analysis between PageRank rankings and official results demonstrat

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Jiang, Lin Cheng, Fang Fang Li, Bin Ge, Wei Dong Xiao, Jiu Yang Tang, and Yan Li Hu. "Detecting Opinion Leaders in Online Communities Based on an Improved PageRank Algorithm." Applied Mechanics and Materials 543-547 (March 2014): 3524–27. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.3524.

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With the rapid development of web 2.0, online communities have become an important way to disclosure and spread the public sentiment. Opinion leaders in online communities play an important role during the formation of public opinion. The paper designs and implements an opinion leader detecting method based on an improved PageRank algorithm. The improved PageRank algorithm uses link relevance to define the weight of the link between users. The first step is crawling data from online communities and preprocessing them. Then construct the weight matrix by calculating link relevance between users

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Tang, Xia, Chun Wen, Xian-Ming Gu, and Zhao-Li Shen. "Anderson Acceleration of the Arnoldi-Inout Method for Computing PageRank." Symmetry 13, no. 4 (2021): 636. http://dx.doi.org/10.3390/sym13040636.

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Anderson(m0) extrapolation, an accelerator to a fixed-point iteration, stores m0+1 prior evaluations of the fixed-point iteration and computes a linear combination of those evaluations as a new iteration. The computational cost of the Anderson(m0) acceleration becomes expensive with the parameter m0 increasing, thus m0 is a common choice in most practice. In this paper, with the aim of improving the computations of PageRank problems, a new method was developed by applying Anderson(1) extrapolation at periodic intervals within the Arnoldi-Inout method. The new method is called the AIOA method.

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Zeng, Jinhui, Yisong Wu, Jie Liu, Dong He, and Zheng Lan. "Identification of Critical Nodes in Power Grid Based on Improved PageRank Algorithm and Power Flow Transfer Entropy." Electronics 13, no. 1 (2023): 184. http://dx.doi.org/10.3390/electronics13010184.

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Identifying critical nodes in the power grid is a crucial aspect of power system security and stability analysis. However, the current methods for identification fall short in fully accounting for the power transfer characteristics between nodes and the consequences of node removal on the security and stability of power grid operation. To enhance the effective and accurate identification of critical nodes in the power grid, a method is proposed. This method is based on improved PageRank algorithm and node-weighted power flow transfer entropy, referred to as IPRA-PFTE. Firstly, based on the pow

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Liu, Li, Letian Sun, Shiping Chen, Ming Liu, and Jun Zhong. "K -PRSCAN: A clustering method based on PageRank." Neurocomputing 175 (January 2016): 65–80. http://dx.doi.org/10.1016/j.neucom.2015.10.020.

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Yin, Jun-Feng, Guo-Jian Yin, and Michael Ng. "On adaptively accelerated Arnoldi method for computing PageRank." Numerical Linear Algebra with Applications 19, no. 1 (2011): 73–85. http://dx.doi.org/10.1002/nla.789.

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Kuchansky, Alexander, Andrii Biloshchytskyi, Yurii Andrashko, Svitlana Biloshchytska, and Adil Faizullin. "The Scientific Productivity of Collective Subjects Based on the Time-Weighted PageRank Method with Citation Intensity." Publications 10, no. 4 (2022): 40. http://dx.doi.org/10.3390/publications10040040.

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This study aims to estimate the scientific productivity of collective subjects. The objective is to build a method for evaluating scientific productivity through calculation, including for new collective subjects with a small citation network—the paper proposes the Time-Weighted PageRank method with citation intensity (TWPR-CI). The Citation Network Dataset (ver. 13) has been analyzed to verify the method. The dataset includes more than 5 million scientific publications and 48 million citations. Four classes of collective subjects (more than 27,000 collective subjects in total) were establishe

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M., Zainal Arifin, Naim Che Pee Ahmad, and Suhaila Rahim Sarni. "Knowing group motivation using Bolzano method on PageRank computation." TELKOMNIKA (Telecommunication, Computing, Electronics and Control) 20, no. 5 (2022): 996–1003. https://doi.org/10.12928/telkomnika.v20i5.19650.

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On the e-learning system, student assignments are collected, but problems arise that based on observations from two classes of database courses, 73% of students make plagiarism so lecturers need to give motivation to students. Self motivate is needed by with a group of students. For this reason, using a bolzano method or bisection method will provide an overview of the development of the plagiarism trend between groups of students based on scores on similarity score that compute by PageRank algorithm used by Google. Research method is carried out by conducting preliminary observations of plagi

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Wang, Meng, Gang Zhou, and Jun Yu Chen. "Analysis of User Influence Using User Behavior and Random Walk." Applied Mechanics and Materials 571-572 (June 2014): 1163–67. http://dx.doi.org/10.4028/www.scientific.net/amm.571-572.1163.

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To improve the effect of user influence predicting in microblog, this paper proposed a new method of user influence analysis named UBRWR, based on user interactive behavior and the random walk method. UBRWR firstly used the behaviors between users to reconstruct the network topology, and then an improved PageRank algorithm was applied to predict the user influence, with quantized individual attribute features. The experimental in Weiba show that the UBRWR algorithm outperforms the PageRank algorithm and method using fans count in terms of ranking accuracy.

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Xie, Yue, Ting-Zhu Huang, Chun Wen, and De-An Wu. "An Improved Approach to the PageRank Problems." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/438987.

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We introduce a partition of the web pages particularly suited to the PageRank problems in which the web link graph has a nested block structure. Based on the partition of the web pages, dangling nodes, common nodes, and general nodes, the hyperlink matrix can be reordered to be a more simple block structure. Then based on the parallel computation method, we propose an algorithm for the PageRank problems. In this algorithm, the dimension of the linear system becomes smaller, and the vector for general nodes in each block can be calculated separately in every iteration. Numerical experiments sho

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Joseph, Gogodze. "PageRank Method for Benchmarking Computational Problems and their Solvers." International Journal of Computer Science Issues 15, no. 3 (2018): 1–7. https://doi.org/10.5281/zenodo.1320053.

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In this short note, we propose a new tool for benchmarking computational problems and their solvers. The proposed tool, which is a version of the PageRank method, is illustrated using an example to demonstrate its viability and suitability for applications.

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Perrin, Dimitri, and Guido Zuccon. "Recursive module extraction using Louvain and PageRank." F1000Research 7 (August 14, 2018): 1286. http://dx.doi.org/10.12688/f1000research.15845.1.

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Biological networks are highly modular and contain a large number of clusters, which are often associated with a specific biological function or disease. Identifying these clusters, or modules, is therefore valuable, but it is not trivial. In this article we propose a recursive method based on the Louvain algorithm for community detection and the PageRank algorithm for authoritativeness weighting in networks. PageRank is used to initialise the weights of nodes in the biological network; the Louvain algorithm with the Newman-Girvan criterion for modularity is then applied to the network to iden

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Parreira, Josiane Xavier, Carlos Castillo, Debora Donato, Sebastian Michel, and Gerhard Weikum. "The Juxtaposed approximate PageRank method for robust PageRank approximation in a peer-to-peer web search network." VLDB Journal 17, no. 2 (2007): 291–313. http://dx.doi.org/10.1007/s00778-007-0057-y.

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Cipolla, Stefano, Carmine Di Fiore, and Francesco Tudisco. "Euler-Richardson method preconditioned by weakly stochastic matrix algebras: a potential contribution to Pagerank computation." Electronic Journal of Linear Algebra 32 (February 6, 2017): 254–72. http://dx.doi.org/10.13001/1081-3810.3343.

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Let S be a column stochastic matrix with at least one full row. Then S describes a Pagerank-like random walk since the computation of the Perron vector x of S can be tackled by solving a suitable M-matrix linear system Mx = y, where M = I â Ï A, A is a column stochastic matrix and Ï is a positive coefficient smaller than one. The Pagerank centrality index on graphs is a relevant example where these two formulations appear. Previous investigations have shown that the Euler- Richardson (ER) method can be considered in order to approach the Pagerank computation problem by means of preconditio

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Biloshchytskyi, Andrii, Oleksandr Kuchanskyi, Aidos Mukhatayev, et al. "Application of Time-Weighted PageRank Method with Citation Intensity for Assessing the Recent Publication Productivity and Partners Selection in R&D Collaboration." Publications 12, no. 4 (2024): 48. https://doi.org/10.3390/publications12040048.

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This article considers the problem of assessing the recent publication productivity of scientists based on PageRank class methods and proposes to use these assessments to solve the problem of selecting scientific partners for R&D projects. The methods of PageRank, Time-Weighted PageRank, and the Time-Weighted PageRank method with Citation Intensity (TWPR-CI) were used as a basis for calculating the publication productivity of individual subjects or scientists. For verification, we used the Citation Network Dataset (Ver. 14) of more than 5 million STEM publications with 36 million citations

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He, Yan Li. "A Novel Heuristic PageRank Algorithm in Web Search." Advanced Materials Research 216 (March 2011): 747–51. http://dx.doi.org/10.4028/www.scientific.net/amr.216.747.

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With the booming development of the Internet, web search engines have become the most important Internet tools for retrieving information. PageRank computes the principal eigenvector of the matrix describing the hyperlinks in the web using the famous power method. Based on empirical distributions of Web page degrees, we derived analytically the probability distribution for the PageRank metric. We found out that it follows the familiar inverse polynomial law reported for Web page degrees.

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Kim, Tae-Hwan, Ho-Chul Jeon, and Joong-Min Choi. "A Reranking Method Using Query Expansion and PageRank Check." KIPS Transactions:PartB 18B, no. 4 (2011): 231–40. http://dx.doi.org/10.3745/kipstb.2011.18b.4.231.

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Arifin, M. Zainal, Ahmad Naim Che Pee, and Sarni Suhaila Rahim. "Knowing group motivation using Bolzano method on PageRank computation." TELKOMNIKA (Telecommunication Computing Electronics and Control) 20, no. 5 (2022): 996. http://dx.doi.org/10.12928/telkomnika.v20i5.19650.

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Srivastava, Atul Kumar, Mitali Srivastava, Rakhi Garg, and Pramod Kumar Mishra. "An Aitken-extrapolated Gauss-Seidel method for computing PageRank." Journal of Statistics and Management Systems 22, no. 2 (2019): 199–222. http://dx.doi.org/10.1080/09720510.2019.1580901.

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Pu, Bing-Yuan, Ting-Zhu Huang, and Chun Wen. "A preconditioned and extrapolation-accelerated GMRES method for PageRank." Applied Mathematics Letters 37 (November 2014): 95–100. http://dx.doi.org/10.1016/j.aml.2014.05.017.

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Gu, Chuanqing, and Lei Wang. "On the multi-splitting iteration method for computing PageRank." Journal of Applied Mathematics and Computing 42, no. 1-2 (2013): 479–90. http://dx.doi.org/10.1007/s12190-013-0645-5.

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Ma, Qianli, Zheng Fan, Chenzhi Wang, and Hongye Tan. "Graph Mixed Random Network Based on PageRank." Symmetry 14, no. 8 (2022): 1678. http://dx.doi.org/10.3390/sym14081678.

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In recent years, graph neural network algorithm (GNN) for graph semi-supervised classification has made great progress. However, in the task of node classification, the neighborhood size is often difficult to expand. The propagation of nodes always only considers the nearest neighbor nodes. Some algorithms usually approximately classify by message passing between direct (single-hop) neighbors. This paper proposes a simple and effective method, named Graph Mixed Random Network Based on PageRank (PMRGNN) to solve the above problems. In PMRGNN, we design a PageRank-based random propagation strate

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Wu, Zongning, Weichen Xu, Shida Yu, Chongchong Yu, Mengxiong Li, and Jingyi Li. "Selecting causal features with higher-order suppression mechanism in compound bearing faults: a perspective of hyper-networks." Measurement Science and Technology 36, no. 6 (2025): 066111. https://doi.org/10.1088/1361-6501/adcf3f.

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Abstract In recent years, complex network analysis has gained widespread application in fault diagnosis and prediction for rolling bearings, particularly in compound fault feature selection. However, the features of compound fault signals are interrelated across different dimensions due to nonlinear superposition, which often results in masking weak fault signal information when hidden interactions among features occur. To address this, we present a novel PageRank algorithm for compound fault feature selection by integrating a higher-order suppression mechanism with hyper-network theory. In th

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Xie, Fei, Jun Yan, and Jun Shen. "A Novel PageRank-Based Fault Handling Strategy for Workflow Scheduling in Cloud Data Centers." International Journal of Web Services Research 18, no. 4 (2021): 1–26. http://dx.doi.org/10.4018/ijwsr.2021100101.

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Unexpected faults result in unscheduled cloud outage, which negatively affects the completion of workflow tasks in the cloud. This paper presents a novel PageRank-based fault handling strategy to rescue workflow tasks at the faulty data center. The proposed approach uses a holistic view and considers the task attributes, the timeline scenario, and the overall cloud performance. A priority assignment system is developed based on the modified PageRank algorithm to prioritise workflow tasks. A min-max normalization method is applied to select the target data center and match the timeline at this

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Tian, Zhaolu, Xiaoyan Liu, Yudong Wang, and P. H. Wen. "The modified matrix splitting iteration method for computing PageRank problem." Filomat 33, no. 3 (2019): 725–40. http://dx.doi.org/10.2298/fil1903725t.

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In this paper, based on the iteration methods [3,10], we propose a modified multi-step power-inner-outer (MMPIO) iteration method for solving the PageRank problem. In the MMPIO iteration method, we use the multi-step matrix splitting iterations instead of the power method, and combine with the inner-outer iteration [24]. The convergence of the MMPIO iteration method is analyzed in detail, and some comparison results are also given. Several numerical examples are presented to illustrate the effectiveness of the proposed algorithm.

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Yang, Yunyun, Gang Xie, and Jun Xie. "Mining Important Nodes in Directed Weighted Complex Networks." Discrete Dynamics in Nature and Society 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/9741824.

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In complex networks, mining important nodes has been a matter of concern by scholars. In recent years, scholars have focused on mining important nodes in undirected unweighted complex networks. But most of the methods are not applicable to directed weighted complex networks. Therefore, this paper proposes a Two-Way-PageRank method based on PageRank for further discussion of mining important nodes in directed weighted complex networks. We have mainly considered the frequency of contact between nodes and the length of time of contact between nodes. We have considered the source of the nodes (in-

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Wen, Chun, Qian-Ying Hu, Bing-Yuan Pu, and Yu-Yun Huang. "Acceleration of an adaptive generalized Arnoldi method for computing PageRank." AIMS Mathematics 6, no. 1 (2021): 893–907. http://dx.doi.org/10.3934/math.2021053.

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Zhang, Hong-Fan, Ting-Zhu Huang, Chun Wen, and Zhao-Li Shen. "FOM accelerated by an extrapolation method for solving PageRank problems." Journal of Computational and Applied Mathematics 296 (April 2016): 397–409. http://dx.doi.org/10.1016/j.cam.2015.09.027.

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Miao, Cun-Qiang, and Xue-Yuan Tan. "Accelerating the Arnoldi method via Chebyshev polynomials for computing PageRank." Journal of Computational and Applied Mathematics 377 (October 2020): 112891. http://dx.doi.org/10.1016/j.cam.2020.112891.

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Xie, Ya-Jun, and Chang-Feng Ma. "A relaxed two-step splitting iteration method for computing PageRank." Computational and Applied Mathematics 37, no. 1 (2016): 221–33. http://dx.doi.org/10.1007/s40314-016-0338-4.

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Han, Xuqian Ben, Shihao Wang, and Chenglong Yu. "PageRank of Gluing Networks and Corresponding Markov Chains." Mathematics 13, no. 13 (2025): 2080. https://doi.org/10.3390/math13132080.

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This paper studies Google’s PageRank algorithm. By an innovative application of the method of gluing Markov chains, we study the properties of Markov chains and extend their applicability by accounting for the damping factor and the personalization vector. Many properties of Markov chains related to spectrums and eigenvectors of the transition matrix, including the stationary distribution, periodicity, and persistent and transient states, will be investigated as well as part of the gluing process. Using the gluing formula, it is possible to decompose a large network into some sub-networks, com

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Tian, Zhaolu, Xiaojing Li, and Zhongyun Liu. "A general multi-step matrix splitting iteration method for computing PageRank." Filomat 35, no. 2 (2021): 679–706. http://dx.doi.org/10.2298/fil2102679t.

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Based on the general inner-outer (GIO) iteration method [5,34] and the iteration framework [6], we present a general multi-step matrix splitting (GMMS) iteration method for computing PageRank, and analyze its overall convergence property. Moreover, the same idea can be used as a preconditioning technique for accelerating the Krylov subspace methods, such as GMRES method. Finally, several numerical examples are given to illustrate the effectiveness of the proposed algorithm.

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