Distributed PageRank Computation Based on Iterative Aggregation-Disaggregation Methods

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Distributed PageRank ComputationBased on
Iterative Aggregation-Disaggregation Methods

• Yangbo Zhu, Shaozhi Ye and Xing Li
• Tsinghua University, Beijing, China
• ACM CIKM 2005, Bremen

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Outline

• Quick Review of PageRank
• Distributed PageRank Computation
• Motivation
• Basic Idea
• Algorithm
• Experiments
• Conclusion and Future Work

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PageRank - Background

• Ranking Web pages
• Content-based methods
• Link-based methods
• PageRank Page Brin, 1998
• HITS Kleinberg, 1998
• SALSA Lempel Moran, 2000

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PageRank - Intuition

• Page A points to B means that the author of A
  recommends B.
• A page is of high quality if it is
• referred to by many other pages
• referred to by pages of high quality

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PageRank - Model

• Random Surfer - Markov Chain

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PageRank - Algorithm

• Power method

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Outline

• Quick Review of PageRank
• Distributed PageRank Computation
• Motivation
• Basic Idea
• Algorithm
• Experiments
• Conclusion and Future Work

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Motivation

• Compass search engine confederation

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Motivation (cont.)
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Basic Idea

• Divide and conquer
• Make use of the natural block structure of web
  graphs

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DPC Algorithm

• Step 1 - Initialization
• Local nodes compute local PageRank vectors.

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DPC Algorithm (cont.)

• Step 2 - Aggregation
• Central node computes the NodeRank vector.

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DPC Algorithm (cont.)

• Step 3 - Disaggregation
• Local nodes compute extended local PageRank
  vectors.

X External nodes
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DPC Algorithm (cont.)

• Step 4 - Central node computes the L1 distance
  between current global PageRank vector and
  previous one.

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Advantages

• DPC mainly consists of standard PageRank
  computation.
• Small matrices fit into main memory.
• Low communication overhead.

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Outline

• Quick Review of PageRank
• Distributed PageRank Computation
• Motivation
• Basic Idea
• Algorithm
• Experiments
• Conclusion and Future Work

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Experimental Setup

• Simulation on a single Linux box.
• Group web pages by sites.
• For comparison
• Classic power method
• LPR-Ref-2 algorithm in Wang, VLDB 2004

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Data Sets

• ST01/03 - crawled in 2001/2003 by Stanford
  WebBase Project
• CN04 - crawled in 2004 from web sites in China.

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Evaluation Metrics

• L1 distance
• Kendall's t-distance
• if page i and j are
  in different order in the two ranking lists.

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Accuracy of the First Iteration

• L1

• Kendall

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Convergence Rate

• Number of iteration
• for convergence
• ( )

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Outline

• Quick Review of PageRank
• Distributed PageRank Computation
• Experiments
• Conclusion and Future Work

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Conclusion

• A distributed PageRank computation algorithm
  based on iterative aggregation-disaggregation
  (IAD) methods with Block Jacobi smoothing.
• Experiments on real web graphs show that DPC
  outperforms LPR-Ref-2Wang, VLDB'04, and
  converges 57 times faster than Power method.

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Future Work

• Implement DPC in distributed system. Integrate
  with Compass search engine confederation.
• How to update PageRank vectors efficiently within
  DPC framework?

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• Thank you !

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General PageRank Algorithm
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IAD Method - Notations

• Aggregation matrix(nN)

• Disaggregation matrix(Nn)

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IAD Method
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DPC Algorithm
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DPC Algorithm (Cont.)
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DPC Algorithm (Cont.)
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DPC -Convergence Analysis

• The global convergence of IAD method is still an
  open problem.
• The difficulty partly comes from that the
  disaggregation step is non-linear.
• The paper proves the global convergence of Block
  Jacobi method in PageRank scenario when n gt 2.

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Experiments - Basic Facts

• Distribution over number of pages hosted by sites
  of different size

• Distribution over size of sites

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Experiments - Communication Overhead
Power
LPR-Ref-2 / DPC

• Pos() - Number of positive elements
• L/U - Block strictly lower/upper triangular part
  of P