SUBSKY: Efficient Computation of Skylines in Subspaces

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SUBSKY Efficient Computation of Skylines in
Subspaces

• Yufei Tao City University of Hong Kong
• Xiaokui Xiao City University of Hong Kong
• Jian Pei Simon Fraser University

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Outline

• Motivation
• Existing solutions
• Our technique
• Experiments
• Conclusion

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Skyline

• Dominate p1 dominates p2.

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Motivation

• The housing relation may contain many other
  attributes
• size
• distances to the nearest super-market / school /
  subway
• security / pollution / traffic ratings of the
  neighborhood

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Motivation (cont.)

• A user wants to retrieve the skyline only in a
  subspace involving a small number of dimensions.
• price and size
• price, distance to the supermarket
• price, security rating
• Why small?
• Skylines are increasingly meaningless as the
  dimensionality grows.

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Existing Solutions

• Non index-based
• require scanning the dataset at least once.
• E.g. Block-nested-loop
• Index-based
• much lower query time.
• State-of-the-art BBS Papadias, Tao, Fu,
  Seeger, ACM TODS 2005

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Our Solution SUBSKY

• Supports any subspace with a single B-tree.
• Can be implemented in relational databases.

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Basic SUBSKY

• Optimized for uniform data.
• Without loss of generality, assume that each
  dimension has a domain 0, 1.
• Define the maximal corner as the point which have
  coordinate 1 on all dimensions
• We convert a d-dimensional point p to a single
  value f(p)

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Basic Property
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Lemma 1

• An example
• d 3
• SUB 1, 2, psky (0.05, 0.1, --)
• f(p)
• e.g., p 0.2, 0.3, 0.25

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Algorithm

• Find the skyline in SUB 1, 2
• Access the points in descending order of their
  f(p).
• p3, p4, p5, p1, p6, p2, p8, p7
• Skyline

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Algorithm (cont.)

• p4, p5, p1, p6, p2, p8, p7
• Skyline p3
• Threshold 0.5

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Algorithm (cont.)

• p5, p1, p6, p2, p8, p7
• Skyline p3, p4
• Threshold 0.5

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Algorithm (cont.)

• p1, p6, p2, p8, p7
• Skyline p3, p4, p5
• Threshold 0.5

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Algorithm (cont.)

• p6, p2, p8, p7
• Skyline p1, p4, p5
• Threshold 0.8

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Algorithm (cont.)

• p2, p8, p7
• Skyline p1, p4, p5
• Threshold 0.8

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Why Does it Work?

• Assume a 15D dataset with 100k points.
• We want to compute the subspace skyline on two
  dimensions.
• There is a high chance that a skylinepoint lies
  very close to the origin inthe subspace.
• For ? 0.001, the probability 90.
• Such a point prunes points lying ina
  15-dimensional square with length0.999.
• I.e., 0.99915 98.5 of the dataset!

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SUBSKY for Arbitrary Distribution

• Anchor

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Assigning a Point to an Anchor
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Selecting the Anchors
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Index Structure

• Use a single B-tree
• Each object is indexed with a composite key ( j,
  f(p) )

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Experiments

• Real datasets
• NBA, 13d, 17k
• Household, 6d, 127k
• Color, 9d, 68k
• Synthetic data
• Uniform, clustered
• Page size 4k bytes

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Experiments (cont.)

• Competitor
• Branch-and-Bound Skyline (BBS)
• state-of-the-art index-based method
• utilize an R-tree
• page size 4k bytes
• Queries
• 100 random subspace queries
• measure the number of page accesses on the B-tree
  (SUBSKY) and the R-tree (BBS)

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Cost vs. Cardinality
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Cost vs. Full Space Dimensionality
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Conclusion

• Subspace skyline computation is often more
  important than retrieval in the full space.
• We developed a fast relational approach for
  processing subspace queries.

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• Thank you!