1. Xu Zhou Kenli Li Yantao Zhou Keqin Li
Adaptive Processing for Distributed Skyline Queries over Uncertain Data
Xu Zhou Kenli Li Yantao Zhou Keqin Li

2. Motivation Increased data uncertainty
Increased distributed data storage systems
More attention towards skyline queries over uncertain data in distributed environments(DSUD query)
Also, DSUD(Distributed Skyline query over Uncertain Data) is a vital research topic with many potential real-life application

3. Problem Statement Many Research achievement on Uncertain Data. But
Most of them focused on single and centralized storage database
Lack adaptations or optimization specific to Distributed environment
Distributed skyline queries are available but mostly in certain data
DSUD query and enhanced-DSUD was first formulated by Ding and Jin[1] with minimized bandwidth consumption and progressiveness
But DSUD query still needs to be improved in three aspects PROGRESSIVENESS, EFFICIENCY, AND UNIVERSALITY

4. Contribution by Authors
Review DSUD query and summarize its objectives
Propose an improved framework for DSUD query with local site pruning
Present an adaptive ( ADSUD) algorithm based on IDSUD framework
Present evaluation of ADSUD algorithm which showed much better efficiency and progressiveness compared to e-DSUD.

5. Skyline query
In a database, a Skyline = set of points which stand out among the others because are of special interest to us
Skyline: those points which are not dominated by any other point.
A point dominates another point if it is as good or better in all dimensions and better in at least one dimension

6. Uncertain Data Data which either exist or doesn’t exist
in the real world
Has an existential probability value
based on which we decide whether it exist
or not in the real world
Here, world1 has existential probability of
0.001% chance it exists actual database
99.99% chance it does not exist in
the actual database.
Fig 1

7. DSUD Query
At first, each local site computes its local skylines, respectively.
Given two local skyline tuples t1 and t2 from local site S1 and t1≻t2, local skyline probability of tuple t2 is
PrLSky(t2)= Pr(t2)(1- (Pr(t1))∏t≻t2,t∈UDBi-t1(1-Pr(t))
Representative Skyline tuple
Uncertain DataBase
UDB1
UDB2
UDBk

8. DSUD Query In server H, let tuple t1≻ t1’in priority queue,
then Local skyline probability of tuple t1’
is refreshed as
PrLSky(t1’)= PrLSky(t1’)(1-(Pr(t1))∏t≻t1’,t∈L-t1(1-Pr(t))
At the start of the second iteration,assume
that tuple t2 is sent to H and t2≻t1’.
The approximate global probability of tuple
t1’ can be computed by
Pr’GSky(t1’)= PrLSky(t1’) x (1- PrLSky(t1))2 x (1-Pr(t2)) x ∏t∈L,t≻t1(1-Pr(t)) x
∏t≻t2,t∈UDBi-t1(1-Pr(t)) x ∏t≻t1’,t∈UDBx∩L-t2[PrLSky(t)(1 - Pr (t) / Pr(t))]
Representative Skyline tuple

9. DSUD Query Finally, DSUD query returns the tuples at H
whose Global Skyline probabilities are not
less than α.
Problem with DSUD
It doesn’t take Total Query Time
into consideration
Its progressiveness also has room
to be improved
Representative Skyline tuple

10. The Improved-DSUD(IDSUD) Framework
GOAL:
Minimize TQT(Total Query Time) & Perform better progressiveness for DSUD query
Improvements:
First, Query-Routing Phase Introduced. Includes:
Site pruning in Query-Routing Phase
Progressive Pruning at each local site
Second, improved PR-tree (IPR-tree)
To boost DSUD
Finally, in To-Server Phase, only one local site representative tuple each time.
New local tuple choosing strategy(MPBR)
MPBR selects multiple representative tuple for each site

11. Adaptive-DSUD(ADSUD) Algorithm
Local Sorting Strategies
Old method to calculate GSky
effective to choose most dominant tuple
Less effective for Local Skyline answers have dominant relationship
New method to calculate approx. global skyline probability
Let UGPrune be the set of unqualified tuples at H
PrNewGSky(t)= PrLSky(t,UDBi) x ∏t’≻t [(1-Pr(t’)) x
PrLSky(t’,UDBk) x ∏t”≻t’ 1/(1-Pr(t”))]
Where, t’ ∊ UDBk∩L, t" ∊ UDBi∩(UGSky ∪ UGPrune) t1 t2 t3
Probability Decreases
If PrNewGSky(t) < α , prune t and refresh the probabilities at H and arrange in descending order. tN
Local Site

12. Minimum Probabilistic Bounding Rectangle(MPBR)
Good skyline algorithm = minm. transfer of unqualified skyline points
Therefore, selection of Local skyline algorithm is very important
MBR of R-tree
MPBR(their local algorithm)
Created usually by clustering the near points
Generated according to the probability threshold
2. Utilized in local-computation phase for improving pruning capacity
2. Used to help choosing the local multiple representative tuples & helps to gain the abstracted info for the site pruning in Query-Routing Phase

13. MPBR Definition: Set of tuples that satisfy the condition
Prnonexist(BR) = ∏tj∊BR(1-Pr(tj)) < α
MPBR-Dominance: Given two MPBRs BR= (tmin,tmax) and BR’ = (t’min, t’max), we have BR ≻ BR’, if tmax ≻ t’min.(tmin,tmax are the minimum and maximum corner of BR)
Lemma 1: Given a MPBR BR = (tmin,tmax) and a tuple t, if tmax ≻ t, then t can be safely pruned.
Lemma 2: Given two MPBRs BR =(tmin, tmax) and BR’ =(t’min, t’max), if BR ≻BR’ , then the tuples contained in BR’ can be safely pruned.

14. MPBR Constrained Space(MPCS)
Definition: For a MPBR set BRS = {1 ≤ i ≤ |BRS||BRi = (timin, timax)} , its MPCS consists of the union of all the regions which are dominated by ti max.
Based on the property of MPCS:
Lemma 3: Given a MPCS CS of a MPBR
set BRS = {1 ≤ i ≤ |BRS||BRi = (timin, timax)}
and a tuple t, if t ∈ CS, the tuple t can be
safely pruned
Lemma 4: Given a MPCS CS and a MPBR
BR = (tmin,tmax), if BR ∈ CS, the tuples
contained in BR can be safely pruned

15. The Local Algorithms
Reduced Local individual processing time = reduced TQT
State-of-the-art Centralized algorithm
The Reuse Mechanism
Reduces I/O operation
Boosts performance
Traditional Methods: Applies window query over R-tree to find skyline result each time
Results in visiting same node many times(larger I/O operation)
Reuse Mechanism: Maintains a Reuse Heap (set of already examined node)

16. The IPR-Tree Indices are built on UDB to improve Query Efficiency by
max(Prmax(PE3),Prmax(PE4))
Prnonexist(PE3) x Prnonexist(PE4)
The IPR-Tree
Indices are built on UDB to
improve Query Efficiency by
reducing the Processing time
In this solution, IPR-Tree is used
Skyline Probability of tuple depends
on:
Its existential probability
Non-existential probability of each entry that dominates it
Existential Probabilities
Fig: Example of an IPR-Tree

17. The LUSQ ALgorithm Computes Skyline at each local site
Uses Progressive pruning Strategy to reduce the Search Space
Two Phases: Pruning & Refining
Pruning: Uses different Lemma for pruning the tuples:
Lemma 5 Given an entity E, if Prmax(E) < α, then tuples within E can be safely pruned.
Lemma 6 Given two entries Ei and Ej, if Ei ≻ Ej and Prmax(Ej) Prnonexist(Ei) < α, the tuples contained in Ej can be safely pruned.
Lemma 7. Given an entry E, in case PrUBLSky(E) < α, tuples within E can be safely pruned.
And others.
Refining: Use the Reuse-Heap(IPR-Tree) to
Find all tuples in Heap that dominates the remaining tuples after pruning
And recalculate their skyline probabilities

18. - used to find global candidate skylines
The GUSQ Algorithm
- used to find global candidate skylines
Uncertain database UDB0
Representative Skyline tuple

19. Performance Evaluation

20. Performance Evaluation

21. Performance Evaluation

22. Conclusion
To accelerate DSUD, improved DSUD framework and new algorithm ADSUD
In ADSUD, several efficient technologies:
IPR-Tree
Reuse Technology
MPBR
Collecting global abstract information
Selecting local representative tuples
Future work: DSUD queries under MapReduce