Dynamic PageRank: Algorithms and Lower Bounds

Authors Rajesh Jayaram , Jakub Łącki , Slobodan Mitrović, Krzysztof Onak , Piotr Sankowski



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Author Details

Rajesh Jayaram
  • Google Research, New York, NY, USA
Jakub Łącki
  • Google Research, New York, NY, USA
Slobodan Mitrović
  • University of California Davis, CA, USA
Krzysztof Onak
  • Boston University, USA
Piotr Sankowski
  • IDEAS NCBR, University of Warsaw, Poland
  • MIM Solutions, Warsaw, Poland

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Rajesh Jayaram, Jakub Łącki, Slobodan Mitrović, Krzysztof Onak, and Piotr Sankowski. Dynamic PageRank: Algorithms and Lower Bounds. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 90:1-90:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.90

Abstract

We consider the PageRank problem in the dynamic setting, where the goal is to explicitly maintain an approximate PageRank vector π ∈ ℝⁿ for a graph under a sequence of edge insertions and deletions. Our main result is a complete characterization of the complexity of dynamic PageRank maintenance for both multiplicative and additive (L₁) approximations. First, we establish matching lower and upper bounds for maintaining additive approximate PageRank in both incremental and decremental settings. In particular, we demonstrate that in the worst-case (1/α)^{Θ(log log n)} update time is necessary and sufficient for this problem, where α is the desired additive approximation. On the other hand, we demonstrate that the commonly employed ForwardPush approach performs substantially worse than this optimal runtime. Specifically, we show that ForwardPush requires Ω(n^{1-δ}) time per update on average, for any δ > 0, even in the incremental setting. For multiplicative approximations, however, we demonstrate that the situation is significantly more challenging. Specifically, we prove that any algorithm that explicitly maintains a constant factor multiplicative approximation of the PageRank vector of a directed graph must have amortized update time Ω(n^{1-δ}), for any δ > 0, even in the incremental setting, thereby resolving a 13-year old open question of Bahmani et al. (VLDB 2010). This sharply contrasts with the undirected setting, where we show that poly log n update time is feasible, even in the fully dynamic setting under oblivious adversary.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
  • Information systems → Page and site ranking
  • Theory of computation → Random walks and Markov chains
  • Mathematics of computing → Graph algorithms
Keywords
  • PageRank
  • dynamic algorithms
  • graph algorithms

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References

  1. Madhav Aggarwal, Bingyi Zhang, and Viktor Prasanna. Performance of local push algorithms for personalized pagerank on multi-core platforms. In 2021 IEEE 28th International Conference on High Performance Computing, Data, and Analytics (HiPC), pages 370-375. IEEE, 2021. Google Scholar
  2. Reid Andersen, Christian Borgs, Jennifer Chayes, John Hopcraft, Vahab S Mirrokni, and Shang-Hua Teng. Local computation of PageRank contributions. In International Workshop on Algorithms and Models for the Web-Graph, pages 150-165. Springer, 2007. Google Scholar
  3. Reid Andersen, Fan Chung, and Kevin Lang. Local graph partitioning using pagerank vectors. In 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06), pages 475-486. IEEE, 2006. Google Scholar
  4. Bahman Bahmani, Abdur Chowdhury, and Ashish Goel. Fast incremental and personalized PageRank. Proc. VLDB Endow., 4(3):173-184, December 2010. URL: https://doi.org/10.14778/1929861.1929864.
  5. Bahman Bahmani, Ravi Kumar, Mohammad Mahdian, and Eli Upfal. PageRank on an evolving graph. In Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining, pages 24-32, 2012. Google Scholar
  6. Marco Bressan, Enoch Peserico, and Luca Pretto. Sublinear algorithms for local graph centrality estimation. In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS), pages 709-718. IEEE, 2018. Google Scholar
  7. Sergey Brin and Lawrence Page. The anatomy of a large-scale hypertextual web search engine. Comput. Netw. ISDN Syst., 30(1-7):107-117, April 1998. URL: https://doi.org/10.1016/S0169-7552(98)00110-X.
  8. Soumen Chakrabarti. Dynamic personalized pagerank in entity-relation graphs. In Proceedings of the 16th international conference on World Wide Web, pages 571-580, 2007. Google Scholar
  9. Wentian Guo, Yuchen Li, Mo Sha, and Kian-Lee Tan. Parallel personalized PageRank on dynamic graphs. Proceedings of the VLDB Endowment, 11(1):93-106, 2017. Google Scholar
  10. Kyung Soo Kim and Yong Suk Choi. Incremental iteration method for fast PageRank computation. In Proceedings of the 9th International Conference on Ubiquitous Information Management and Communication, IMCOM '15, New York, NY, USA, 2015. Association for Computing Machinery. URL: https://doi.org/10.1145/2701126.2701165.
  11. Qun Liao, ShuangShuang Jiang, Min Yu, Yulu Yang, and Tao Li. Monte Carlo based incremental PageRank on evolving graphs. In Pacific-Asia Conference on Knowledge Discovery and Data Mining, pages 356-367. Springer, 2017. Google Scholar
  12. Peter Lofgren. On the complexity of the monte carlo method for incremental pagerank. Inf. Process. Lett., 114(3):104-106, 2014. URL: https://doi.org/10.1016/J.IPL.2013.11.006.
  13. Peter Lofgren, Siddhartha Banerjee, and Ashish Goel. Personalized pagerank estimation and search: A bidirectional approach. In Proceedings of the Ninth ACM International Conference on Web Search and Data Mining, pages 163-172, 2016. Google Scholar
  14. Peter Lofgren and Ashish Goel. Personalized PageRank to a target node. arXiv preprint, 2013. URL: https://arxiv.org/abs/1304.4658.
  15. Peter A Lofgren, Siddhartha Banerjee, Ashish Goel, and C Seshadhri. FAST-PPR: Scaling personalized PageRank estimation for large graphs. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, pages 1436-1445, 2014. Google Scholar
  16. Jakub Łącki, Slobodan Mitrović, Krzysztof Onak, and Piotr Sankowski. Walking randomly, massively, and efficiently. In Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, pages 364-377, 2020. Google Scholar
  17. Amit Pathak, Soumen Chakrabarti, and Manish Gupta. Index design for dynamic personalized pagerank. In 2008 IEEE 24th International Conference on Data Engineering, pages 1489-1491. IEEE, 2008. Google Scholar
  18. Ryan A Rossi and David F Gleich. Dynamic pagerank using evolving teleportation. In International Workshop on Algorithms and Models for the Web-Graph, pages 126-137. Springer, 2012. Google Scholar
  19. Subhajit Sahu, Kishore Kothapalli, and Dip Sankar Banerjee. Dynamic batch parallel algorithms for updating pagerank. In 2022 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), pages 1129-1138. IEEE, 2022. Google Scholar
  20. Scott Sallinen, Juntong Luo, and Matei Ripeanu. Real-time pagerank on dynamic graphs. In Proceedings of the 32nd International Symposium on High-Performance Parallel and Distributed Computing, pages 239-251, 2023. Google Scholar
  21. Hanzhi Wang, Zhewei Wei, Junhao Gan, Sibo Wang, and Zengfeng Huang. Personalized PageRank to a target node, revisited. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pages 657-667, 2020. Google Scholar
  22. Hanzhi Wang, Zhewei Wei, Ji-Rong Wen, and Mingji Yang. Revisiting local computation of pagerank: Simple and optimal. In STOC'24, 2024. Google Scholar
  23. Xindong Wu, Vipin Kumar, J. Ross Quinlan, Joydeep Ghosh, Qiang Yang, Hiroshi Motoda, Geoffrey J. McLachlan, Angus Ng, Bing Liu, Philip S. Yu, Zhi-Hua Zhou, Michael Steinbach, David J. Hand, and Dan Steinberg. Top 10 algorithms in data mining. Knowledge and Information Systems, 14(1):1-37, January 2008. URL: https://doi.org/10.1007/s10115-007-0114-2.
  24. Zexing Zhan, Ruimin Hu, Xiyue Gao, and Nian Huai. Fast incremental pagerank on dynamic networks. In International Conference on Web Engineering, pages 154-168. Springer, 2019. Google Scholar
  25. Hongyang Zhang, Peter Lofgren, and Ashish Goel. Approximate personalized PageRank on dynamic graphs. In Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, pages 1315-1324, 2016. Google Scholar