skip to main content
research-article

Efficient Algorithms for Approximate Single-Source Personalized PageRank Queries

Authors Info & Claims
Published:23 October 2019Publication History
Skip Abstract Section

Abstract

Given a graph G, a source node s, and a target node t, the personalized PageRank (PPR) of t with respect to s is the probability that a random walk starting from s terminates at t. An important variant of the PPR query is single-source PPR (SSPPR), which enumerates all nodes in G and returns the top-k nodes with the highest PPR values with respect to a given source s. PPR in general and SSPPR in particular have important applications in web search and social networks, e.g., in Twitter’s Who-To-Follow recommendation service. However, PPR computation is known to be expensive on large graphs and resistant to indexing. Consequently, previous solutions either use heuristics, which do not guarantee result quality, or rely on the strong computing power of modern data centers, which is costly.

Motivated by this, we propose effective index-free and index-based algorithms for approximate PPR processing, with rigorous guarantees on result quality. We first present FORA, an approximate SSPPR solution that combines two existing methods—Forward Push (which is fast but does not guarantee quality) and Monte Carlo Random Walk (accurate but slow)—in a simple and yet non-trivial way, leading to both high accuracy and efficiency. Further, FORA includes a simple and effective indexing scheme, as well as a module for top-k selection with high pruning power. Extensive experiments demonstrate that the proposed solutions are orders of magnitude more efficient than their respective competitors. Notably, on a billion-edge Twitter dataset, FORA answers a top-500 approximate SSPPR query within 1s, using a single commodity server.

References

  1. Reid Andersen, Christian Borgs, Jennifer T. Chayes, John E. Hopcroft, Vahab S. Mirrokni, and Shang-Hua Teng. 2007. Local computation of PageRank contributions. In Proceedings of the WAW. 150--165.Google ScholarGoogle ScholarCross RefCross Ref
  2. Reid Andersen, Fan R. K. Chung, and Kevin J. Lang. 2006. Local graph partitioning using PageRank vectors. In Proceedings of the FOCS. 475--486.Google ScholarGoogle Scholar
  3. Konstantin Avrachenkov, Nelly Litvak, Danil Nemirovsky, Elena Smirnova, and Marina Sokol. 2011. Quick detection of Top-k personalized PageRank lists. In Proceedings of the WAW. 50--61.Google ScholarGoogle ScholarCross RefCross Ref
  4. Lars Backstrom and Jure Leskovec. 2011. Supervised random walks: Predicting and recommending links in social networks. In Proceedings of the WSDM. 635--644.Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Bahman Bahmani, Kaushik Chakrabarti, and Dong Xin. 2011. Fast personalized PageRank on MapReduce. In Proceedings of the SIGMOD. 973--984.Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Pavel Berkhin. 2005. Survey: A survey on PageRank computing. Int. Math. 2, 1 (2005), 73--120.Google ScholarGoogle ScholarCross RefCross Ref
  7. Deepayan Chakrabarti, Yiping Zhan, and Christos Faloutsos. 2004. R-MAT: A recursive model for graph mining. In Proceedings of the SDM. 442--446.Google ScholarGoogle ScholarCross RefCross Ref
  8. Fan R. K. Chung and Lincoln Lu. 2006. Survey: Concentration inequalities and martingale inequalities: A survey. Int. Math. 3, 1 (2006), 79--127.Google ScholarGoogle ScholarCross RefCross Ref
  9. Dániel Fogaras, Balázs Rácz, Károly Csalogány, and Tamás Sarlós. 2005. Towards scaling fully personalized PageRank: Algorithms, lower bounds, and experiments. Int. Math. 2, 3 (2005), 333--358.Google ScholarGoogle ScholarCross RefCross Ref
  10. Yasuhiro Fujiwara, Makoto Nakatsuji, Hiroaki Shiokawa, Takeshi Mishima, and Makoto Onizuka. 2013. Efficient ad hoc search for personalized PageRank. In Proceedings of the SIGMOD. 445--456.Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Yasuhiro Fujiwara, Makoto Nakatsuji, Takeshi Yamamuro, Hiroaki Shiokawa, and Makoto Onizuka. 2012. Efficient personalized PageTank with accuracy assurance. In Proceedings of the KDD. 15--23.Google ScholarGoogle Scholar
  12. Manish S. Gupta, Amit Pathak, and Soumen Chakrabarti. 2008. Fast algorithms for top-k personalized PageRank queries. In Proceedings of the WWW. 1225--1226.Google ScholarGoogle Scholar
  13. 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 WWW. 505--514.Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Taher H. Haveliwala. 2002. Topic-sensitive PageRank. In Proceedings of the WWW. 517--526.Google ScholarGoogle Scholar
  15. Kalervo Järvelin and Jaana Kekäläinen. 2000. IR evaluation methods for retrieving highly relevant documents. In Proceedings of the SIGIR. 41--48.Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Glen Jeh and Jennifer Widom. 2003. Scaling personalized web search. In Proceedings of the WWW. 271--279.Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Peter Lofgren. 2015. Efficient algorithms for personalized PageRank. Retrieved from: CoRR abs/1512.04633 (2015).Google ScholarGoogle Scholar
  18. Peter Lofgren, Siddhartha Banerjee, and Ashish Goel. 2016. Personalized PageRank estimation and search: A bidirectional approach. In Proceedings of the WSDM. 163--172.Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Peter A. Lofgren, Siddhartha Banerjee, Ashish Goel, and C. Seshadhri. 2014. FAST-PPR: Scaling personalized PageRank estimation for large graphs. In Proceedings of the KDD. 1436--1445.Google ScholarGoogle Scholar
  20. Takanori Maehara, Takuya Akiba, Yoichi Iwata, and Ken-ichi Kawarabayashi. 2014. Computing personalized PageRank quickly by exploiting graph structures. PVLDB 7, 12 (2014), 1023--1034.Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Naoto Ohsaka, Takanori Maehara, and Ken-ichi Kawarabayashi. 2015. Efficient PageRank tracking in evolving networks. In Proceedings of the SIGKDD. 875--884.Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Lawrence Page, Sergey Brin, Rajeev Motwani, and Terry Winograd. 1999. The PageRank Citation Ranking: Bringing Order to the Web. Technical Report. Stanford University, Stanford, CA.Google ScholarGoogle Scholar
  23. Atish Das Sarma, Anisur Rahaman Molla, Gopal Pandurangan, and Eli Upfal. 2013. Fast distributed PageRank computation. In Proceedings of the ICDCN. 11--26.Google ScholarGoogle Scholar
  24. Kijung Shin, Jinhong Jung, Lee Sael, and U. Kang. 2015. BEAR: Block elimination approach for random walk with restart on large graphs. In Proceedings of the SIGMOD. 1571--1585.Google ScholarGoogle Scholar
  25. Sibo Wang, Youze Tang, Xiaokui Xiao, Yin Yang, and Zengxiang Li. 2016. HubPPR: Effective indexing for approximate personalized PageRank. PVLDB 10, 3 (2016), 205--216. Retrieved from: http://www.vldb.org/pvldb/vol10/p205-wang.pdf.Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Sibo Wang and Yufei Tao. 2018. Efficient algorithms for finding approximate heavy hitters in personalized PageRanks. In Proceedings of the SIGMOD. 1113--1127.Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. 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 SIGKDD. 505--514.Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. 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 SIGMOD. 1042--1059.Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. 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 SIGMOD. 441--456.Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Minji Yoon, Jinhong Jung, and U. Kang. 2018. TPA: Fast, scalable, and accurate method for approximate random walk with restart on billion scale graphs. In Proceedings of the ICDE.Google ScholarGoogle Scholar
  31. Hongyang Zhang, Peter Lofgren, and Ashish Goel. 2016. Approximate personalized PageRank on dynamic graphs. In Proceedings of the KDD. 1315--1324.Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Fanwei Zhu, Yuan Fang, Kevin Chen-Chuan Chang, and Jing Ying. 2013. Incremental and accuracy-aware personalized PageRank through scheduled approximation. PVLDB 6, 6 (2013), 481--492.Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Efficient Algorithms for Approximate Single-Source Personalized PageRank Queries

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in

    Full Access

    • Published in

      cover image ACM Transactions on Database Systems
      ACM Transactions on Database Systems  Volume 44, Issue 4
      Best of EDBT 2017, Best of EDBT 2018, Best of ICDT 2018 and Regular Papers
      December 2019
      249 pages
      ISSN:0362-5915
      EISSN:1557-4644
      DOI:10.1145/3366712
      Issue’s Table of Contents

      Copyright © 2019 ACM

      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 23 October 2019
      • Accepted: 1 August 2019
      • Revised: 1 March 2019
      • Received: 1 August 2018
      Published in tods Volume 44, Issue 4

      Permissions

      Request permissions about this article.

      Request Permissions

      Check for updates

      Qualifiers

      • research-article
      • Research
      • Refereed

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    HTML Format

    View this article in HTML Format .

    View HTML Format