An Optimal and Progressive Algorithm for Skyline Queries

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An Optimal and Progressive Algorithm for Skyline
Queries

• Presenter Jongwuk Lee
• Information Database Systems Lab.
• POSTECH

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Contents

• Introduction
• Skyline queries
• Existing solutions
• Motivation
• Algorithms BBS
• Other discussions

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Finding the Cheapest Closest Hotels
price

• Which one is better?
• i and h?
• i, because its price and distance dominate those
  of h.
• i and k?
• I do not know.

y
10
b
e
9
a
c
8
7
d
6
g
f
5
l
h
n
4
3
2
i
k
m
1
x
o
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2
3
4
5
6
7
8
9
10
distance
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Skyline Objects

• A set of objects not dominated by any other
  objects.
• Dominating region

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Existing Solutions

• Block Nested Loop (BNL)
• Divide-and-Conquer (DC)
• Bitmap method
• Index method
• Nearest Neighbor (NN)

Elementary skyline algorithms
Progressive skyline algorithms
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Existing Solutions

• Block Nested Loop (BNL)
• Scan the dataset and keep a list of candidate
  skyline points.
• Compare a point p with every other point in the
  list.
• Advantages
• Wide applicability
• Disadvantages
• Numerous comparisons, inadequacy for on-line
  processing

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Existing Solutions

• Divide-and-Conquer (DC)
• Divide the dataset into several partitions.
• Compute partial skylines in each partition.
• Compute global skylines by merging them.

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Existing Solutions

• Nearest Neighbor (NN)
• Find nearest neighbor point.
• Divide the space by the nearest neighbor point.
• Compute recursively until empty space.

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Existing Solutions

• NN over three or more dimensions
• Has overlapped partitions in divided subspaces.
• Needs duplicate elimination.

NN partitions for 3 dimensions
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Motivation

• Advantages of NN algorithm
• Fast running time to finding the first result
• Progressiveness
• Disadvantages of NN algorithm
• Redundant I/O computation
• Explosive to-do list size
• Goal Improve NN algorithm and offer useful
  variations.

Do you think there exists more efficient and
useful skyline algorithm?
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Contents

• Introduction
• Algorithms BBS
• Preliminary R-Tree
• How BBS works on
• Example
• Other Discussions

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R-Tree Clustering by Proximity
Root
E
E
1
2
E
E
E
E
E
E
1
E
3
4
5
6
7
2
e
a
c
d
g
b
f
m
j
l
i
h
k
E
E
E
E
E
4
3
5
7
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R-Tree
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R-Tree
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Branched and Bound Skyline (BBS)

• Assume all points are indexed in an R-tree.
• Top-down Approach
• mindist the L1 distance between its lower-left
  corner and the origin.

f(x, y) x y
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Branched and Bound Skyline (BBS)

• Data structure
• Heap by min distance
• List to maintain the current skyline
• Dominance check condition
• Before expanding or inserting, compare to current
  skylines.
• Before inserting an object, also check for
  internal objects.
• Stop condition empty heap

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Example of BBS

• Each heap entry keeps the mindist of the MBR.

access root
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Example of BBS

• Process entries in ascending order of their
  mindists.

access root
expand e7
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Example of BBS
access root
expand e7
expand e3
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Example of BBS
access root
expand e7
expand e3
remove e6
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Example of BBS
access root
expand e7
expand e3
remove e6
remove e5
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Example of BBS
access root
expand e7
expand e3
remove e6
remove e5
expand e1
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Example of BBS
access root
expand e7
expand e3
remove e6
remove e5
expand e1
expand e4
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Contents

• Introduction
• Algorithms BBS
• Other Discussions
• Constrained skyline queries
• K-dominating queries

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Constrained Skyline Queries
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Constrained Skyline Queries
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Constrained Skyline Queries
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Constrained Skyline Queries
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Constrained Skyline Queries
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K-dominating Queries

• Retrieve 3 points that dominate the largest
  number of other points.

h and m may dominate at most 7 points. (num(i)
2)
num(i) 9, num(a)2, num(k)2
3-dominating result i
3-dominating result i
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K-dominating Queries
num(h) 7, num(m)5, num(a)2, num(k)2
c and g may dominate at most 5 points. (num(h)
2)
3-dominating result i, h, m
2-dominating result i, h
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Thats it.
QA
Thank you!