research-article

Estimating Single-Node PageRank in Õ (min{d_t, √m}) Time

Authors:

Zhewei WeiAuthors Info & Claims

Proceedings of the VLDB Endowment, Volume 16, Issue 11

Pages 2949 - 2961

https://doi.org/10.14778/3611479.3611500

Published: 01 July 2023 Publication History

Abstract

PageRank is a famous measure of graph centrality that has numerous applications in practice. The problem of computing a single node's PageRank has been the subject of extensive research over a decade. However, existing methods still incur large time complexities despite years of efforts. Even on undirected graphs where several valuable properties held by PageRank scores, the problem of locally approximating the PageRank score of a target node remains a challenging task. Two commonly adopted techniques, Monte-Carlo based random walks and backward push, both cost O(n) time in the worst-case scenario, which hinders existing methods from achieving a sublinear time complexity like O(√m) on an undirected graph with n nodes and m edges.

In this paper, we focus on the problem of single-node PageRank computation on undirected graphs. We propose a novel algorithm, SetPush, for estimating single-node PageRank specifically on undirected graphs. With non-trival analysis, we prove that our SetPush achieves the Õ (min {d_t, √m]}) time complexity for estimating the target node t's PageRank with constant relative error and constant failure probability on undirected graphs. We conduct comprehensive experiments to demonstrate the effectiveness of SetPush.

References

[1]

[n.d.]. http://arxiv.org/abs/2307.13162.

[2]

Reid Andersen, Christian Borgs, Jennifer Chayes, John Hopcraft, Vahab S Mirrokni, and Shang-Hua Teng. 2007. Local computation of PageRank contributions. In International Workshop on Algorithms and Models for the Web-Graph. Springer, 150--165.

[3]

Reid Andersen, Fan R. K. Chung, and Kevin J. Lang. 2006. Local Graph Partitioning using PageRank Vectors. In FOCS. 475--486.

[4]

Konstantin Avrachenkov, Nelly Litvak, Danil Nemirovsky, and Natalia Osipova. 2007. Monte Carlo methods in PageRank computation: When one iteration is sufficient. SIAM J. Numer. Anal. 45, 2 (2007), 890--904.

Digital Library

[5]

Bahman Bahmani, Abdur Chowdhury, and Ashish Goel. 2010. Fast incremental and personalized pagerank. arXiv preprint arXiv:1006.2880 (2010).

[6]

Andrey Balmin, Vagelis Hristidis, and Yannis Papakonstantinou. 2004. Objectrank: Authority-based keyword search in databases. In VLDB, Vol. 4. 564--575.

[7]

Ziv Bar-Yossef and Li-Tal Mashiach. 2008. Local approximation of pagerank and reverse pagerank. In Proceedings of the 17th ACM conference on Information and knowledge management. 279--288.

Digital Library

[8]

Aleksandar Bojchevski, Johannes Klicpera, Bryan Perozzi, Amol Kapoor, Martin Blais, Benedek Rózemberczki, Michal Lukasik, and Stephan Günnemann. 2020. Scaling Graph Neural Networks with Approximate PageRank. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, New York, NY, USA.

Digital Library

[9]

Paolo Boldi, Francesco Bonchi, Carlos Castillo, Debora Donato, Aristides Gionis, and Sebastiano Vigna. 2008. The query-flow graph: model and applications. In Proceedings of the 17th ACM conference on Information and knowledge management. 609--618.

Digital Library

[10]

Marco Bressan, Enoch Peserico, and Luca Pretto. 2018. Sublinear algorithms for local graph centrality estimation. In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 709--718.

[11]

Karl Bringmann and Konstantinos Panagiotou. 2012. Efficient sampling methods for discrete distributions. In International colloquium on automata, languages, and programming. Springer, 133--144.

[12]

Moses Charikar, Kevin Chen, and Martin Farach-Colton. 2002. Finding frequent items in data streams. In International Colloquium on Automata, Languages, and Programming. Springer, 693--703.

Digital Library

[13]

Ming Chen, Zhewei Wei, Zengfeng Huang, Bolin Ding, and Yaliang Li. 2020. Simple and deep graph convolutional networks. In International Conference on Machine Learning. PMLR, 1725--1735.

[14]

Fan Chung. 2007. The heat kernel as the pagerank of a graph. Proceedings of the National Academy of Sciences 104, 50 (2007), 19735--19740.

[15]

Luc Devroye. 2006. Nonuniform random variate generation. Handbooks in operations research and management science 13 (2006), 83--121.

[16]

Dániel Fogaras. 2003. Where to start browsing the web?. In International Workshop on Innovative Internet Community Systems. Springer, 65--79.

[17]

Dániel Fogaras, Balázs Rácz, Károly Csalogány, and Tamás Sarlós. 2005. Towards scaling fully personalized pagerank: Algorithms, lower bounds, and experiments. Internet Mathematics 2, 3 (2005), 333--358.

[18]

David F Gleich. 2015. PageRank beyond the Web. siam REVIEW 57, 3 (2015), 321--363.

[19]

Pankaj Gupta, Ashish Goel, Jimmy Lin, Aneesh Sharma, Dong Wang, and Reza Zadeh. 2013. Wtf: The who to follow service at twitter. In Proceedings of the 22nd international conference on World Wide Web. 505--514.

Digital Library

[20]

Taher Haveliwala and Sepandar Kamvar. 2003. The second eigenvalue of the Google matrix. Technical Report. Stanford.

[21]

Glen Jeh and Jennifer Widom. 2003. Scaling personalized web search. In Proceedings of the 12th international conference on World Wide Web. 271--279.

Digital Library

[22]

Johannes Klicpera, Aleksandar Bojchevski, and Stephan Günnemann. 2019. Predict then Propagate: Graph Neural Networks meet Personalized PageRank. In ICLR.

[23]

Kyle Kloster and David F Gleich. 2014. Heat kernel based community detection. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining. 1386--1395.

Digital Library

[24]

Haewoon Kwak, Changhyun Lee, Hosung Park, and Sue Moon. 2010. What is Twitter, a social network or a news media?. In Proceedings of the 19th international conference on World wide web. 591--600.

Digital Library

[25]

Peter Lofgren. 2015. EFFICIENT ALGORITHMS FOR PERSONALIZED PAGERANK. Ph.D. Dissertation. STANFORD UNIVERSITY.

[26]

Peter Lofgren, Siddhartha Banerjee, and Ashish Goel. 2015. Bidirectional pagerank estimation: From average-case to worst-case. In Algorithms and Models for the Web Graph: 12th International Workshop, WAW 2015, Eindhoven, The Netherlands, December 10--11, 2015, Proceedings 12. Springer, 164--176.

Digital Library

[27]

Peter Lofgren, Siddhartha Banerjee, and Ashish Goel. 2016. Personalized pagerank estimation and search: A bidirectional approach. In Proceedings of the Ninth ACM International Conference on Web Search and Data Mining. 163--172.

Digital Library

[28]

Peter Lofgren and Ashish Goel. 2013. Personalized pagerank to a target node. arXiv preprint arXiv:1304.4658 (2013).

[29]

Peter A Lofgren, Siddhartha Banerjee, Ashish Goel, and C Seshadhri. 2014. Fast-ppr: Scaling personalized pagerank estimation for large graphs. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining. 1436--1445.

Digital Library

[30]

Michael Mitzenmacher and Eli Upfal. 2017. Probability and computing: Randomization and probabilistic techniques in algorithms and data analysis. Cambridge university press.

[31]

Barbara Logan Mooney, L René Corrales, and Aurora E Clark. 2012. MoleculaR-networks: An integrated graph theoretic and data mining tool to explore solvent organization in molecular simulation. Journal of computational chemistry 33, 8 (2012), 853--860.

[32]

Julie L Morrison, Rainer Breitling, Desmond J Higham, and David R Gilbert. 2005. GeneRank: using search engine technology for the analysis of microarray experiments. BMC bioinformatics 6, 1 (2005), 1--14.

[33]

Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd. 1999. The PageRank citation ranking: bringing order to the web. (1999).

[34]

J Michael Steele. 2004. The Cauchy-Schwarz master class: an introduction to the art of mathematical inequalities. Cambridge University Press.

[35]

Shang-Hua Teng et al. 2016. Scalable algorithms for data and network analysis. Foundations and Trends® in Theoretical Computer Science 12, 1--2 (2016), 1--274.

[36]

Hanzhi Wang, Zhewei Wei, Junhao Gan, Sibo Wang, and Zengfeng Huang. 2020. Personalized pagerank to a target node, revisited. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 657--667.

Digital Library

[37]

Sibo Wang, Renchi Yang, Xiaokui Xiao, Zhewei Wei, and Yin Yang. 2017. FORA: simple and effective approximate single-source personalized pagerank. In Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 505--514.

Digital Library

[38]

Zhewei Wei, Xiaodong He, Xiaokui Xiao, Sibo Wang, Yu Liu, Xiaoyong Du, and Ji-Rong Wen. 2019. Prsim: Sublinear time simrank computation on large power-law graphs. In Proceedings of the 2019 International Conference on Management of Data. 1042--1059.

Digital Library

[39]

Zhewei Wei, Xiaodong He, Xiaokui Xiao, Sibo Wang, Shuo Shang, and Ji-Rong Wen. 2018. Topppr: top-k personalized pagerank queries with precision guarantees on large graphs. In Proceedings of the 2018 International Conference on Management of Data. 441--456.

Digital Library

[40]

Neil A Weiss. 2005. A course in probability. 2005., 385--386 pages.

[41]

Wenpu Xing and Ali Ghorbani. 2004. Weighted pagerank algorithm. In Proceedings. Second Annual Conference on Communication Networks and Services Research, 2004. IEEE, 305--314.

[42]

Renchi Yang, Xiaokui Xiao, Zhewei Wei, Sourav S Bhowmick, Jun Zhao, and Rong-Hua Li. 2019. Efficient estimation of heat kernel pagerank for local clustering. In Proceedings of the 2019 International Conference on Management of Data. 1339--1356.

Digital Library

[43]

Xi-Nian Zuo, Ross Ehmke, Maarten Mennes, Davide Imperati, F Xavier Castellanos, Olaf Sporns, and Michael P Milham. 2012. Network centrality in the human functional connectome. Cerebral cortex 22, 8 (2012), 1862--1875.

Cited By

Liu HLuo S(2024)BIRD: Efficient Approximation of Bidirectional Hidden Personalized PageRankProceedings of the VLDB Endowment10.14778/3665844.366585517:9(2255-2268)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.14778/3665844.3665855
Wang HBaeza-Yates RBonchi F(2024)Revisiting Local PageRank Estimation on Undirected Graphs: Simple and OptimalProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671820(3036-3044)Online publication date: 25-Aug-2024
https://dl.acm.org/doi/10.1145/3637528.3671820
Yang MWang HWei ZWang SWen J(2024)Efficient Algorithms for Personalized PageRank Computation: A SurveyIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2024.337600036:9(4582-4602)Online publication date: Sep-2024
https://doi.org/10.1109/TKDE.2024.3376000

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Published In

cover image Proceedings of the VLDB Endowment

Proceedings of the VLDB Endowment Volume 16, Issue 11

July 2023

789 pages

ISSN:2150-8097

Editors:
Georgia Koutrika
Athena Research Center
,
Jun Yang
Duke University

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VLDB Endowment

Publication History

Published: 01 July 2023

Published in PVLDB Volume 16, Issue 11

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Cited By

Liu HLuo S(2024)BIRD: Efficient Approximation of Bidirectional Hidden Personalized PageRankProceedings of the VLDB Endowment10.14778/3665844.366585517:9(2255-2268)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.14778/3665844.3665855
Wang HBaeza-Yates RBonchi F(2024)Revisiting Local PageRank Estimation on Undirected Graphs: Simple and OptimalProceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining10.1145/3637528.3671820(3036-3044)Online publication date: 25-Aug-2024
https://dl.acm.org/doi/10.1145/3637528.3671820
Yang MWang HWei ZWang SWen J(2024)Efficient Algorithms for Personalized PageRank Computation: A SurveyIEEE Transactions on Knowledge and Data Engineering10.1109/TKDE.2024.337600036:9(4582-4602)Online publication date: Sep-2024
https://doi.org/10.1109/TKDE.2024.3376000

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