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Approximating Single-Source Personalized PageRank with Absolute Error Guarantees

Authors Zhewei Wei , Ji-Rong Wen , Mingji Yang

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Author Details

Zhewei Wei
  • Renmin University of China, Beijing, China
Ji-Rong Wen
  • Renmin University of China, Beijing, China
Mingji Yang
  • Renmin University of China, Beijing, China

Funding

This work was partially done at Gaoling School of Artificial Intelligence, Peng Cheng Laboratory, Beijing Key Laboratory of Big Data Management and Analysis Methods, and MOE Key Lab of Data Engineering and Knowledge Engineering. This research was supported in part by National Natural Science Foundation of China (No. U2241212, No. 61972401, No. 61932001, No. 61832017, No. U2001212), the major key project of PCL (PCL2021A12), Beijing Natural Science Foundation (No. 4222028), Beijing Outstanding Young Scientist Program No.BJJWZYJH012019100020098, Alibaba Group through Alibaba Innovative Research Program, and Huawei-Renmin University joint program on Information Retrieval.

Acknowledgements

We also wish to acknowledge the support provided by Engineering Research Center of Next-Generation Intelligent Search and Recommendation, Ministry of Education. Finally, we thank the anonymous reviewers for their valuable comments.

Cite As Get BibTex

Zhewei Wei, Ji-Rong Wen, and Mingji Yang. Approximating Single-Source Personalized PageRank with Absolute Error Guarantees. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ICDT.2024.9

Abstract

Personalized PageRank (PPR) is an extensively studied and applied node proximity measure in graphs. For a pair of nodes s and t on a graph G = (V,E), the PPR value π(s,t) is defined as the probability that an α-discounted random walk from s terminates at t, where the walk terminates with probability α at each step. We study the classic Single-Source PPR query, which asks for PPR approximations from a given source node s to all nodes in the graph. Specifically, we aim to provide approximations with absolute error guarantees, ensuring that the resultant PPR estimates π̂(s,t) satisfy max_{t ∈ V} |π̂(s,t)-π(s,t)| ≤ ε for a given error bound ε. We propose an algorithm that achieves this with high probability, with an expected running time of  
- Õ(√m/ε) for directed graphs, where m = |E|; 
- Õ(√{d_max}/ε) for undirected graphs, where d_max is the maximum node degree in the graph; 
- Õ(n^{γ-1/2}/ε) for power-law graphs, where n = |V| and γ ∈ (1/2,1) is the extent of the power law.  These sublinear bounds improve upon existing results. We also study the case when degree-normalized absolute error guarantees are desired, requiring max_{t ∈ V} |π̂(s,t)/d(t)-π(s,t)/d(t)| ≤ ε_d for a given error bound ε_d, where the graph is undirected and d(t) is the degree of node t. We give an algorithm that provides this error guarantee with high probability, achieving an expected complexity of Õ(√{∑_{t ∈ V} π(s,t)/d(t)}/ε_d). This improves over the previously known O(1/ε_d) complexity.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Graph Algorithms
  • Sublinear Algorithms
  • Personalized PageRank

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