Algorithms and Models for the Web-Graph
Volume 4863 of the series Lecture Notes in Computer Science pp 150-165
Local Computation of PageRank Contributions
- Reid AndersenAffiliated withUniversity of California at San Diego, San Diego, CA
- , Christian BorgsAffiliated withMicrosoft Research, Redmond, WA
- , Jennifer ChayesAffiliated withMicrosoft Research, Redmond, WA
- , John HopcraftAffiliated withCornell University, Ithaca, NY
- , Vahab S. MirrokniAffiliated withMicrosoft Research, Redmond, WA
- , Shang-Hua TengAffiliated withBoston University, Boston, MA
Abstract
Motivated by the problem of detecting link-spam, we consider the following graph-theoretic primitive: Given a webgraph G, a vertex v in G, and a parameter δ ∈ (0,1), compute the set of all vertices that contribute to v at least a δ fraction of v’s PageRank. We call this set the δ-contributing set of v. To this end, we define the contribution vector of v to be the vector whose entries measure the contributions of every vertex to the PageRank of v. A local algorithm is one that produces a solution by adaptively examining only a small portion of the input graph near a specified vertex. We give an efficient local algorithm that computes an ε-approximation of the contribution vector for a given vertex by adaptively examining O(1/ε) vertices. Using this algorithm, we give a local approximation algorithm for the primitive defined above. Specifically, we give an algorithm that returns a set containing the δ-contributing set of v and at most O(1/δ) vertices from the δ/2-contributing set of v, and which does so by examining at most O(1/δ) vertices. We also give a local algorithm for solving the following problem: If there exist k vertices that contribute a ρ-fraction to the PageRank of v, find a set of k vertices that contribute at least a (ρ − ε)-fraction to the PageRank of v. In this case, we prove that our algorithm examines at most O(k/ε) vertices.
- Title
- Local Computation of PageRank Contributions
- Book Title
- Algorithms and Models for the Web-Graph
- Book Subtitle
- 5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007. Proceedings
- Pages
- pp 150-165
- Copyright
- 2007
- DOI
- 10.1007/978-3-540-77004-6_12
- Print ISBN
- 978-3-540-77003-9
- Online ISBN
- 978-3-540-77004-6
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- 4863
- Series ISSN
- 0302-9743
- Publisher
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Topics
- Industry Sectors
- eBook Packages
- Editors
- Authors
-
- Reid Andersen (1)
- Christian Borgs (2)
- Jennifer Chayes (2)
- John Hopcraft (3)
- Vahab S. Mirrokni (2)
- Shang-Hua Teng (4)
- Author Affiliations
-
- 1. University of California at San Diego, San Diego, CA,
- 2. Microsoft Research, Redmond, WA,
- 3. Cornell University, Ithaca, NY,
- 4. Boston University, Boston, MA,
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