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An efficient elimination strategy for solving PageRank problems

Author

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  • Shen, Zhao-Li
  • Huang, Ting-Zhu
  • Carpentieri, Bruno
  • Gu, Xian-Ming
  • Wen, Chun

Abstract

In Web link structures, similar link distributions often occur, especially for pages from same hosts. For PageRank problems, similar in-link distributions of pages result in similar row patterns of the transition matrix. We demonstrate that common row patterns in the transition matrix determine identical sub-rows. Thus the identical sub-rows with a large proportion of nonzeros can be eliminated to decrease the density of PageRank problems. We propose an elimination strategy that exploits such identical sub-rows and generates an elimination operator for transferring the problem to an equivalent but more sparse problem. Numerical experiments are reported to illustrate the effectiveness of this strategy for decreasing the computational cost of solving PageRank problems.

Suggested Citation

  • Shen, Zhao-Li & Huang, Ting-Zhu & Carpentieri, Bruno & Gu, Xian-Ming & Wen, Chun, 2017. "An efficient elimination strategy for solving PageRank problems," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 111-122.
    • Handle: RePEc:eee:apmaco:v:298:y:2017:i:c:p:111-122
    DOI: 10.1016/j.amc.2016.10.031
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    Cited by:

    1. Del Corso, Gianna M. & Romani, Francesco, 2019. "Adaptive nonnegative matrix factorization and measure comparisons for recommender systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 164-179.
    2. Tian, Zhaolu & Liu, Yong & Zhang, Yan & Liu, Zhongyun & Tian, Maoyi, 2019. "The general inner-outer iteration method based on regular splittings for the PageRank problem," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 479-501.
    3. Shen, Zhao-Li & Su, Meng & Carpentieri, Bruno & Wen, Chun, 2022. "Shifted power-GMRES method accelerated by extrapolation for solving PageRank with multiple damping factors," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    4. Aleja, David & Criado, Regino & García del Amo, Alejandro J. & Pérez, Ángel & Romance, Miguel, 2019. "Non-backtracking PageRank: From the classic model to hashimoto matrices," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 283-291.

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