The σ-neighborhood skyline queries Chen, Yi-Chung; LEE, Chiang. The σ-neighborhood skyline queries. Information Sciences, 2015, 322: 張天彥 2015/12/05

Outline Introduction to skyline queries The σ-Neighborhood Skyline Queries k-dominant Skyline Conclusions 1

Introduction to skyline queries The concept of domination Distance Price A B C C1.8km$13 Distance to the beach Price of a hotel room Distance to the beach Price of a hotel room A dominates B and C

Introduction to skyline queries Definition of the skyline points Find all points are not dominated by other points 3

Introduction to skyline queries Definition of the skyline points Find all points are not dominated by other points 4

Introduction to skyline queries Definition of the skyline points Distance Price A A B B F F D D E E H H G G C C Find all points are not dominated by other points 5

Outline Introduction to skyline queries The σ-Neighborhood Skyline Queries k-dominant Skyline 6

The σ-Neighborhood Skyline Queries Problem to be solved by σ-N Skyline Queries Unquantifiable attributes Distance Price A A B B C C D D E E F F G G H H I I Unquantifiable attributeQuantifiable attribute 7

The σ-Neighborhood Skyline Queries σ-N Skyline Queries Distance Price A A B B F F D D E E H H G G C C 0.2km $2 σ-N skyline region σ-N skyline point I can tolerant 10% error $2 in price, 0.2km in distance 8

The σ-Neighborhood Skyline Queries Applied the σ-N Skyline query in a dataset with unquantifiable attribute Distance Price A B F D E HG C …… The user can tolerant 10% error ($2 in price 0.2km in distance) 9

The σ-Neighborhood Skyline Queries Difficulties of finding σ-N Skyline Queries Distance Price A B F D E HG C Naïve algorithm 1. Find the skyline points by the existing skyline algorithms  first scan 2. Find the σ-N skyline points by the skyline points  second scan Assume there are 1M data points in the dataset  2M data points need to be check 10

The σ-Neighborhood Skyline Queries Difficulties of finding σ-N Skyline Queries Distance Price A B F D E HG C Naïve algorithm 1. Find the skyline points by the existing skyline algorithms  first scan 2. Find the σ-N skyline points by the skyline points  second scan Assume there are 1M data points in the dataset  2M data points need to be check The cost can be too high to afford when the dataset is large Can we solve the σ- N Skyline query in one scan? Can we solve the σ-N Skyline query without scanning all data points in the dataset? 11

The σ-Neighborhood Skyline Queries The algorithms for the σ-N Skyline Queries 12 Rσ-N algorithm (based on R-tree) Mσ-N algorithm (based on M + -tree) Existing indexed structureNewly developed indexed structure Same searching idea Two pruning mechanisms

The σ-Neighborhood Skyline Queries R-tree s2 p2 p3 p4 p1 Example: 13 R-tree is constructed based on the size of area s3 s1 p5 e1 e3 e2 e4 e5e6 e7 e5 e1 e2 s1s2 p1p2 e6 e3 e4 p3p4 s3p5 e7

The σ-Neighborhood Skyline Queries Searching idea s2 p2 p3 p4 p1 Example: 14 Objective: Find skyline points and σ-N Skyline points in one scan s3 s1 p5 e1 e3 e2 e5 e4 e6 e7 e5 e1 e2 s1s2 p1p2 e6 e3 e4 p3p4 s3p5 e7

The σ-Neighborhood Skyline Queries Searching idea Example: 15 Objective: Find skyline points and σ-N Skyline points in one scan e7 e5 e1 e2 s1s2 p1p2 e6 e3 e4 p3p4 s3p5 e7

The σ-Neighborhood Skyline Queries Searching idea Example: 16 Objective: Find skyline points and σ-N Skyline points in one scan e5e6 e5 e1 e2 s1s2 p1p2 e6 e3 e4 p3p4 s3p5 e7 e5 e6 e7

The σ-Neighborhood Skyline Queries Searching idea Example: 17 Objective: Find skyline points and σ-N Skyline points in one scan e1 e2 e5e6 e5 e1 e2 s1s2 p1p2 e6 e3 e4 p3p4 s3p5 e7 e1 e2

The σ-Neighborhood Skyline Queries Searching idea s2 Example: 18 Objective: Find skyline points and σ-N Skyline points in one scan s1 e1 e2 e6 e5 e1 e2 s1s2 p1p2 e6 e3 e4 p3p4 s3p5 e7 s1s2 Range query: e2 v.s. s1 & s2

The σ-Neighborhood Skyline Queries Searching idea s2 p2 p1 Example: 19 Objective: Find skyline points and σ-N Skyline points in one scan s1 e2 e6 e5 e1 e2 s1s2 p1p2 e6 e3 e4 p3p4 s3p5 e7 p1p2 Range query: p1 v.s. s1 & s2 p1 Range query: p2 v.s. s1 & s2 Range query: e2 v.s. s1 & s2 Range query: e6 v.s. s1 & s2

The σ-Neighborhood Skyline Queries Disadvantages of Rσ-N algorithm 20 1.Too many redundant points (Caused by the property of R-tree) R-tree is constructed based on the size of area 1.Too many redundant points (Caused by the property of R-tree) R-tree is constructed based on the size of area e1 e2 Insert into e1 or e2? Insert into e1 or e2? Ans: e1 Insert into e1 or e2? Insert into e1 or e2? e1 e2 Ans: e2 Unrelated points

The σ-Neighborhood Skyline Queries Disadvantages of Rσ-N algorithm Too many redundant points s1s2 Additional I/O cost Additional range queries

The σ-Neighborhood Skyline Queries Disadvantages of Rσ-N algorithm Too many range queries s1s1s2s2s3s3s4s4s5s5 s6s6 A B e1 e1 v.s. s1 ? e1 v.s. s2 ? e1 v.s. s3 ? e1 v.s. s4 ? e1 v.s. s5 ? e1 v.s. s6 ? A v.s. s1 ? A v.s. s2 ? A v.s. s3 ? A v.s. s4 ? A v.s. s5 ? A v.s. s6 ? B v.s. s1 ? B v.s. s2 ? B v.s. s3 ? B v.s. s4 ? B v.s. s5 ? B v.s. s6 ?

The σ-Neighborhood Skyline Queries Using M + -tree to solve the problems R-tree is constructed based on the area M + -tree is constructed based on the distance 23 Related points

The σ-Neighborhood Skyline Queries Using M + -tree to solve the problems R-tree is constructed based on the area M + -tree is constructed based on the distance 24 Number of redundant points

The σ-Neighborhood Skyline Queries Using M + -tree to solve the problems Triangle inequality Skyline point s A, center of M + BR B C σ Only C needs further check 25 Number of redundant points <7

The σ-Neighborhood Skyline Queries Using M + -tree to solve the problems e1 v.s. s6 ? e1 v.s. s5 ? e1 v.s. s4 ? e1 v.s. s3 ? e1 v.s. s2 ? e1 v.s. s1 ? Original: e1 v.s. s1, s2, s3, s4, s5, s6 A v.s. s1, s2, s3, s4, s5, s6 B v.s. s1, s2, s3, s4, s5, s6  18 times of range query s1s1s2s2s3s3s4s4s5s5 s6s6 A B e1 summation 26 A v.s. s6 ? A v.s. s1 ? B v.s. s6 ? B v.s. s1 ?  10 times of range query Number of range queries Easy to get the summation of e1 Summation line

The σ-Neighborhood Skyline Queries Simulations Number of data points: 1M Number of dimensions: 2, 3, 4, 5, 6 Number of data points: 1M Number of dimensions: 2, 3, 4, 5, 6 Independent dataset Anti-correlated dataset 27

The σ-Neighborhood Skyline Queries Simulations- selection of σ Independent dataset Anti-correlated dataset 28

The σ-Neighborhood Skyline Queries Simulations 29

The σ-Neighborhood Skyline Queries Conclusion 10 using the Mσ-N algorithm in σ-N skyline queries is far more efficient than the Rσ-N algorithm.

Outline Introduction to skyline queries The σ-Neighborhood Skyline Queries k-dominant Skyline 30

k-dominant skylines k-dominant skylines 有利於在高維資料減少 支配 skylines 點集數量 Distance Price A B C D E F G H I K L k-Dominant Skylines 31