1 Continuous k-dominant Skyline Query Processing Presented by Prasad Sriram Nilu Thakur

2 Outline Introduction Problem definition Key Concepts Validation Rewrite Today

3 Example Skyline Which one is better? e or b? (e, because its price and distance dominate those of b) C or f? Finding skyline of hotel, lesser price & closer to the beach Distance Pricea b c d e f

4 Problem Definition Input A set of points, p 1,p 2,…p n Output A set of points P (referred to as the skyline points), such that any point p 1 Є P is not dominated by any other point in the dataset Objective Provide correct and complete results Minimize the query response time and memory consumption Continuous queries require continuous evaluation Scalability in terms of the number of queries Constraints Minimize the number of dominance checks

5 Skyline Properties (1/2) Meaningful for incomparable dimensions Browsing Laptops Price, weight, size, memory, etc. Insensitive to scaling and shifting of the dimensions Skyline - Curse of Dimensionality Movie Rating Different users may have different rating preferences Movie p better than q only if p rated higher or equal to q by all users One outlier opinion will invalidate the dominance

6 Skyline Properties (2/2) Too many skyline points in high dimensional spaces Example: NBA data set, player season statistics on 17 attributes Over 1000 skyline points in the full space Some average-skilled players are in the skyline if they are not bad on some attributes. Possible Solutions Dimension Reduction Techniques - Requires domain knowledge Subspace Skylines - Many subspaces need to be explored Relax the notion of d-dominance - k-dominance

7 k-dominant Skyline k-Dominate If A is not worse than B on k dimensions, and better on at least one of the k dimensions, we say A k- dominates B. k-Dominant Skyline k-dominant skyline contains all the points that cannot be k-dominated by any other point k-Dominant Skyline Query Given a data set, find the k-dominant skyline When k=d, we have the conventional skyline K-dominance is cyclic unlike d-dominance

Slide Courtesy [2]8 k-dominant Skyline - Example d1d2d3d4d5d6 p p p p p conventional skyline 5-dominant skyline 4-dominant skyline Smaller k, smaller k-dominant skyline

9 Cyclic Properties of k-dominance k-dominance can be cyclic A 3-dominates B d1d2d3d4 A5555 B1666 C2177 D3218

10 Cyclic Properties of k-dominance B 3-dominates C d1d2d3d4 A5555 B1666 C2177 D3218

11 Cyclic Properties of k-dominance C 3-dominates D d1d2d3d4 A5555 B1666 C2177 D3218

12 Cyclic Properties of k-dominance D 3-dominates A d1d2d3d4 A5555 B1666 C2177 D3218

13 Skyline Evaluation Techniques – A Taxonomy Static vs Continuous Index-based vs Non-Index based Euclidean distance vs Road Network distance Geometric Properties Ranked skyline queries Constrained skyline queries Enumerating queries k-dominating queries k-dominant queries

14 A naïve approach Case 1 A new point arrives It is k-dominated by some points It k-dominates some points Case 2 A point expires

15 An improved approach a(1) b(3) c(5) d(7)e(9)f(11)g(13) Skyline heapNon-Skyline heap

16 An improved approach a(1) b(3) c(5) d(7)e(9)f(11)g(13) Skyline heapNon-Skyline heap h(15) h(26) a16DIS b18DIS c20DIS d22DIS e24DIS f26DIS g28DIS h26RET

17 An improved approach b(3) d(7) c(5) e(9)f(11)g(13) Skyline heapNon-Skyline heap h(26) b18DIS c20DIS d22DIS e24DIS f26DIS g28DIS h26RET at t = 16

18 An improved approach b(3) d(7) c(5) e(9)f(11)g(13) Skyline heapNon-Skyline heap h(26) b18DIS c20DIS d22DIS e24DIS f26DIS g28DIS i20RET i(17) i(20)

19 An improved approach c(5) d(7) f(11) e(9)g(13) Skyline heapNon-Skyline heap i(20) c20DIS d22DIS e24DIS f26DIS g28DIS i20RET at t = 18

20 An improved approach c(5) d(7) f(11) e(9)g(13) Skyline heapNon-Skyline heap i(20) c20DIS d22DIS e24DIS f26DIS g28DIS i20RET j(19)

21 An improved approach c(5) d(7) f(11) e(9)g(13) Skyline heapNon-Skyline heap i(20) c20DIS d22DIS e24DIS f26DIS g28DIS i20RET j32RET j(32)

22 Validations Methodology  Theorem based proving for correctness and completeness  Experiments to analyze performance Validation criteria  Query Response time

23 Experimental Analysis

24 Rewrite today Improvements A better technique for k-dominance Conduct detailed experiments with network object generators Think about how to find (spatial) skyline in road networks

25 References 1. Yufei Tao, Dimitris Papadias: Maintaining Sliding Window Skylines on Data Streams. IEEE Trans. Knowl. Data Eng. 18(2): (2006) 2. Chee Yong Chan, H. V. Jagadish, Kian-Lee Tan, Anthony K. H. Tung, Zhenjie Zhang: Finding k-dominant skylines in high dimensional space. SIGMOD Conference 2006: M. Sharifzadeh, C. Shahabi. The Spatial Skyline Queries. In Proceedings of VLDB’ Michael D. Morse, Jignesh M. Patel, William I. Grosky: Efficient Continuous Skyline Computation. ICDE 2006: Zhiyong Huang, Hua Lu, Beng Chin Ooi, Anthony K.H. Tung, Continuous Skyline Queries for Moving Objects, IEEE Transactions on Knowledge and Data Engineering, vol. 18, no. 12, pp , Dec., S. Borzsonyi, D. Kossmann, and K. Stocker. The Skyline Operator. In Proceedings of ICDE' D. Kossmann, F. Ramsak, and S. Rost. Shooting Stars in the Sky: An Online Algorithm for Skyline Queries. In Proceedings of VLDB'02.