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Skyline Queries

- HKU CSIS DB Seminar
- 9 April 2003
- Speaker Eric Lo

Skyline

- A new operator in database systems
- Filters out a set of interesting points from a

potential large set of data points - A data point is interesting if it is not

dominated by any other point

Example

- Find some good places for us to hold the next DB

Seminar - Dataset (Table Homes)

- Good ? Close to HKU (Min.)
- Good ? Max. Area (Max.)
- Return those homes that are not worse than any

others in ALL DIMENSIONS

Outline

- Introduction to Skyline Queries
- Skyline Operator in SQL
- Implementation Algorithms
- Progressive Algorithms
- Variations of Skyline Queries
- Experimental Result
- Conclusion

The Skyline OperatorICDE 2001S.Borzonyi,

D.Kossmann, K.Stocker

- Define the skyline operator in databases
- Extension of SQL for skyline
- Block-nested-loop Algorithm
- Divide-and-conquer Algorithm

Problem Definition

- Related to
- maximum vector problem
- contour problem
- convex hull of a data set
- Assume the whole dataset fits in the memory

SQL Extensions

- SELECT FROM WHERE GROUP BY HAVING

SKYLINE OF DISTINCT d1 MIN MAX,

dm MIN MAXORDER BY - d1 dm denote the dimensions participate the

Skyline - SELECT FROM HOMESWHERE CITYHKSKYLINE OF

DIST MIN, AREA MAX

Naïve Approach for Skyline

- 1D skyline is equivalent to computing min, max in

SQL - Naïve 2D skyline
- Sort the data according to the 2 dimensions
- Compare every tuple with its predecessor
- Sorting may need in 2 or more passes if the data

are not fit into memory ? use current external

sorting techniques

Naïve 2D

- Sort by Distance
- Compare Felix with Kevin ? eliminate Felix
- Compare KK with Kevin ? incompatible ? part

of skyline - Compare Ben with KK ? eliminate Ben

Naïve 2D not works for gt 2Ds

- If skyline involves more than 2D, sorting does

not work

Block-nested-loops Algorithm

- A straightforward approach
- Compare each point p with every other point
- If p is not dominated ? part of skyline
- Scan the data file and keeping a list of

candidate skyline points in main memory

BNL cont.

- Insert the 1st data point into the list
- For each subsequent point p
- If p is dominated by any point in the list, it is

discarded - If p dominates any point in the list, insert it

into the list and remove all points dominated by

p - If p neither dominated, nor dominates any point

in the list, inserted it as part of the skyline

in the list

BNL cont.

- The candidate list is self-organizing
- Points that have been dominated other points are

moved to the top of list - Reduces the number of comparisons
- E.g. the self-organizing list holdings the

partial skyline like

More on BNL

- Point 3 in BNL If p neither dominated, nor

dominates any point in the list, inserted it as

part of the skyline in the list. If the are no

more space in the list, write p on a temporary

file on disk. Tuples in tmp file will be further

processed in next iteration of algorithm

More on BNL (cont.)

Dom. by A

After 1st Iteration, A,E,G,H areoutput as

skylines, then clear upthe list and treat I,J

as newdata set and perform BNL again

Dom. by A

G

Dom. by A

Incompatible with A

Incompatible with A,E

Dom On F, replace F

Incompatible with A,E,G

Incompatible with A,E,G,H, but full! Incompatible

with A,E,G,H, but full!J has not compare with I

Short summary on BNL

- Easy to implement
- Any dimension without using index or sorting
- Relies on main memory ? may have many iterations
- Not adequate for on-line processing ? it has to

read the entire data file before it returns the

first skyline point (not progressively)

Divide-and-Conquer Algorithm

- Find the median of some dimension, sayprice,

Price(med)0.3 - Split the input into 2 partitions according to

Price(med) - Compute Skyline S1 in P1(lt0.3) and S2 in

P2(gt0.3) respectively by recursive

partitioning.Note S1 is better than S2 on

price - Recursive partitioning until a partition contains

very few (or 1) tuples - If only a few tuples, find out skyline is very

easy - Merging the skylines of each partitionsby

eliminating those S2 which are dominated by

S1Note None of the tuples in S1 can be

dominatedby S2 as all tuples in S1 are better

than S2 on pricei.e. tuples in UPPER never be

eliminated

Divide-and-Conquer Algorithm

- Find the median of some dimension, sayprice,

Price(med)0.3 - Split the input into 2 partitions according to

Price(med)

Divide-and-Conquer Algorithm

S1

S2

S3

S4

S5

S6

S7

Divide-and-Conquer Algorithm

S1

S2

S1, S2

S3

S1,S2, S7

i.e. tuples in UPPER never be eliminated

S4

S5

S4, S5, S7

S6

S7

Efficient Progressive Skyline ComputationVLDB

2001K.L. Tan, P.K. Eng, B.C. Ooi

- Previous approach require at least one
- pass over the dataset to return the first
- interesting point, We propose
- Bitmap-based Algorithm
- B-tree-based Algorithm
- They can return the first interesting point once
- they identified.

Progressive?

- Both bitmap and tree-base returns skyline very

quickly - Maybe useful if you are not willing to wait so

long for the first few interesting homes out of

the large dataset - Also outperform BNL and D--C in overall response

time

Skyline by Bitmap

- Main idea
- Given a point p, if something can tell you
- p is not dominated by any other points in DB ?

skyline! - p is dominated by some points in DB ? throw away
- Non-blocking!
- Can return the skyline points immediately

Bitmap

- All information requires to decide whether a

point is in skyline are encoded in bitmaps - A data point p (p1, p2, , pd) where d is no.

of dimensions, is mapped to a m-bit vector, m is

number of distinct values over all dimensions

Bitmap

- Distinct values on price and distance is 7 and 4
- m 11

Bitmap representation

- Distinct value on x 10
- Distinct value on y 10
- m20
- 20-bit vector
- E.g (4,8)
- 4 is 4-th smallest on dimension x, set 4-th to

the leftmost be 1 (starting from right) - 8 is 8-th smallest on y, set 8-th to the leftmost

be 1)

Bitmap representation

- Do (4,8) is a skyline point? (min x, y)
- Create bit-strings Cx and Cy (Not CY Ng!)
- Cx 1110000110000
- Cy 0011011111111
- Cx Cy 0010000110000
- If CxCy has more than one 1, dominated by some

points

Bitmap representation

- Do (3,2) is a skyline point? (min x, y)
- Create bit-strings Cx and Cy
- Cx 1100000010000
- Cy 0000000011010
- Cx Cy 0000000010000
- If CxCy has only 1, it is a skyline

Short summary on Bitmap

- Need to pre-compute bitmap representation of

every point - Each point retrieve all bitmaps in order to get

the juxtapositions (Cx and Cy) - Large storage if the domain of each attributes

are large

Some other progressive algorithms

- B-tree index (also proposed by BOC)
- Organizes the points into d lists (d is no. of

dimensions in data) - Build Btree on the lists for retrieving skylines
- Suffer similar problem as bitmap approach

Some other progressive algorithms (cont.)

- NN algorithm (by Donald Kossmann again)
- VLDB 02

NN skyline

Outline

- Introduction to Skyline Queries
- Skyline Operator in SQL
- Implementation Algorithms
- Progressive Algorithms
- Variations of Skyline Queries
- Experimental Result
- Conclusion

An Optimal and Progressive Algorithm for Skyline

QueriesSIGMOD 2003D.Papadias, Y. Tao, G. Fu, B.

Seeger

- We propose
- A NN algorithm which is more efficient andI/O

Optimal - Ranked skyline queries
- Constrained skyline queries
- Dynamic skyline queries
- K-dominating queries

Ranked Skyline

- A ranked skyline returns K skyline points that

have minimum/max score according to a function f - In our example, f 3Dist 7Area
- Return the top K homes
- Though skylines are returning interesting points,

we may want the most interesting points according

to our own preferences, especially the data set

is large(say hotels) and skyline is also large!

Constrained Skyline

- Returning the most interesting points in a

specific data space

Dynamic Skyline

- Returning update skyline dynamically
- E.g. Ask for hotels with minimum distance and

price (again?) - Minimum distance is now depends on my current

location

Enumerating Skyline

- Enumerate queries return, for each skyline point

p, the number of points dominated by p - Sometime useful if you want to know this skyline

hotel C has dominated 1000 hotels, and another

hotel Y dominated only 1 hotel - maybe C is better than Y in many properties (e.g.

price, dist, etc), but Y has only 1 properties

better than C, e.g. with PS2

Experimental Evaluation

- Running time comparison on progressive algorithms

without NN approaches

BNL

DC

Bitmap

Index

Conclusion

- Introduction the skyline queries
- How to implement (support) the skyline operator

in DBMS? - Variation of skyline queries
- If the information are placed in different

places, how to answer skyline queries on a mobile

device?

References

- S.Borzonyi, D.Kossmann, K.Stocker. The Skyline

Operator. ICDE 2001. - K.L. Tan, P.K. Eng, B.C. Ooi . Efficient

Progressive Skyline Computation. VLDB 2001. - D.Kossmann, F.Ramsak, S. Rost. Shooting Stars in

the Sky An Online Algorithm for Skyline Queries.

VLDB 2002. - D.Papadias, Y. Tao, G. Fu, B. Seeger. An Optimal

and Progressive Algorithm for Skyline Queries.

SIGMOD 2003.

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