Skyline Query Processing for Incomplete Data

Mohamed E. Khalefa Mohamed F. Mokbel Justin J. LevandoskiDepartment of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, USAICDE 2008

Skyline Query Processing for Incomplete Data1OutlineIntroductionProblem FormulationMethods and AlgorithmsExperiment ResultsConclusion2IntroductionExisting skyline algorithms assume: 1. Date are complete (all dimensions are available for all data ) 2.Transitive relation.

p1 dominates p2, p2 dominates p3 => p3 dominates p1.

p1(2,3,6)p2(1,2,4)p3(1,1,1)3(Cont.)If data is incomplete: 1.Some dimensions are no value. 2.No transitive relation.

p1 dominates p2, p2 dominates p3.But p1 dont dominates p3. p3 dominates p1.Cycle and no transitive relation!!

p1(2,3,-)p2(1,-,8)p3(-,4,2)4Problem FormulationDominance Relation for Incomplete data: 1.There is at least one dimension ui where both P.ui and Q.ui are known, and P.ui > Q.ui . 2.For all other dimensions j, j i, either P.uj is unknown, Q.uj is unknown, or P.uj Q.uj .Example:

p1 dominates p2. p2 dont domninate p3, and p3 dont domninate p2.

p1(2,3,-)p2(1,-,8)p3(-,4,-)5(Cont.)Bitmap representation:0: unknown dimension 1:know dimension example:

p1.B and p2.B=100Remoed P. 2.If P is dominated by virtual point in Local skyline =>Insert to shadow skyline point. 3.If P is local skyline point=>Insert to the Candidate skyline.( Phase II)Phase II:the number of the Candidate skyline>t=>Insert to the global skyline

16(Cont.)Global skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)t=2P1(6,4,-)Candidate skyline17(Cont.)Global skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)t=2P1Candidate skyline18P1(6,4,-)(Cont.)Global skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)t=2P1(6,4,-)P1Candidate skyline19(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(8,-,1)t=2P1(6,4,-)P1 Q1Q1(9,-,1)20(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)t=2P1(6,4,-)P1 Q1Q1(9,-,1)21(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)t=2P1(6,4,-)P1 Q1Q1(9,-,1)22Q1v(9,-,-)Shadow skylineP1(6,4,-)(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)R1(-,3,1)t=2P1(6,4,-)Q1 R1Q1(9,-,1)23Q1v(9,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)R1(-,3,1)P2(9,3,-)t=2P1(6,4,-)Q1 R1Q1(9,-,1)24Q1v(9,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)R1(-,3,1)P2(9,3,-)t=2P1(6,4,-)Q1 R1 P2Q1(9,-,1)25Q1v(9,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)|Candidate skyline|>2Insert to Global skyline(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(8,-,1)R1(-,3,1)P2(9,3,-)t=2P1(6,4,-)Q1(9,-,1)26Q1v(8,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)Q1 R1 P2Compare against Shadow skyline(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(8,-,1)R1(-,3,1)P2(9,3,-)t=2P1(6,4,-)Q1(9,-,1)27Q1v(8,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)Q1 R1 P2R1 is dominated by P1(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)R1(-,3,1)P2(9,3,-)t=2P1(6,4,-) Q1 P2Q1(9,-,1)28Q1v(9,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)R1(-,3,1)P2(9,3,-)Q2(6,-,1)t=2P1(6,4,-) Q1 P2Q1(9,-,1)29Q1v(9,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)R1(-,3,1)P2(9,3,-)Q2(6,-,1)t=2P1(6,4,-) Q1 P2Q1(9,-,1)30Q1v(9,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)Q2(6,-,1)(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)R1(-,3,1)P2(9,3,-)Q2(6,-,1)R2(-,6,5)t=2P1(6,4,-) Q1 P2Q1(9,-,1)31Q1v(9,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)Q2(6,-,1)R2(-,6,5)(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)R1(-,3,1)P2(9,3,-)Q2(6,-,1)R2(-,6,5)t=2P1(6,4,-) Q1 P2Q1(9,-,1)32Q1v(9,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)Q2(6,-,1)R2 dominates R1R2(-,6,5)(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)R1(-,3,1)P2(9,3,-)Q2(6,-,1)R2(-,6,5)t=2P1(6,4,-) Q1 P2Q1(9,-,1)33Q1v(9,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)Q2(6,-,1)R2(-,6,5)R2Check Candidate skyline and Global skyline

(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)R1(-,3,1)P2(9,3,-)Q2(6,-,1)R2(-,6,5)t=2P1(6,4,-) Q1 P2Q1(9,-,1)34Q1v(9,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)Q2(6,-,1)R2(-,6,5)R2Q1 and P2 are dominated by R2

(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)R1(-,3,1)P2(9,3,-)Q2(6,-,1)R2(-,6,5)t=2P1(6,4,-) Q1(9,-,1)35Q1v(9,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)Q2(6,-,1)R2(-,6,5)R2Global skyline: Global skyline Candidate skyline

(Cont.)Global skylineCandidate skylineNode P = 110Node Q= 101Node R= 011P1(6,4,-)Q1(9,-,1)R1(-,3,1)P2(9,3,-)Q2(6,-,1)R2(-,6,5)t=2P1(6,4,-) Q1(9,-,1)36Q1v(9,-,-)Shadow skylineP1(6,4,-)R1(-,3,1)P2(9,3,-)Q2(6,-,1)R2(-,6,5)R2Result is Global skyline:Q2

Experiment Results37(Cont.)38

(Cont.)39

ConclusionBase on traditional skyline Query: the Replacement Algorithm and the Bucket Algorithm.New method: the ISkyline Algorithm.The performance of the ISkyline Algorithm is the best of three.

40bucketdominate bucket40