Finding Top-k Min-Cost Connected Trees in Databases Bolin Ding 1 - PowerPoint PPT Presentation

Outline Finding Top-k Min-Cost Connected Trees in Databases Bolin Ding 1 Jeffrey Xu Yu 1 Shan Wang 2 Lu Qin 1 Xiao Zhang 2 Xuemin Lin 3 1 Department of System Engineering and Engineering Management The Chinese University of Hong Kong 2 School of Informaion Renmin University of China 3 School of Computer Science and Engineering The University of New South Wales IEEE 23rd International Conference on Data Engineering Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Outline Outline Keyword Search in Relational Databases 1 Database Graph, Query, and Answer The Hardness of This Problem Our New Parameterized Solutions 2 Finding Top-1 Answer Finding Top-k Answers Existing Solutions 3 Other Graph-Based Solutions Experimental Studies 4 Some Representative Experimental Results Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Outline Outline Keyword Search in Relational Databases 1 Database Graph, Query, and Answer The Hardness of This Problem Our New Parameterized Solutions 2 Finding Top-1 Answer Finding Top-k Answers Existing Solutions 3 Other Graph-Based Solutions Experimental Studies 4 Some Representative Experimental Results Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Outline Outline Keyword Search in Relational Databases 1 Database Graph, Query, and Answer The Hardness of This Problem Our New Parameterized Solutions 2 Finding Top-1 Answer Finding Top-k Answers Existing Solutions 3 Other Graph-Based Solutions Experimental Studies 4 Some Representative Experimental Results Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Outline Outline Keyword Search in Relational Databases 1 Database Graph, Query, and Answer The Hardness of This Problem Our New Parameterized Solutions 2 Finding Top-1 Answer Finding Top-k Answers Existing Solutions 3 Other Graph-Based Solutions Experimental Studies 4 Some Representative Experimental Results Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Introduction Parameterized Solution Model Existing Solutions Hardness Experimental Studies Summary Outline Keyword Search in Relational Databases 1 Database Graph, Query, and Answer The Hardness of This Problem Our New Parameterized Solutions 2 Finding Top-1 Answer Finding Top-k Answers Existing Solutions 3 Other Graph-Based Solutions Experimental Studies 4 Some Representative Experimental Results Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Introduction Parameterized Solution Model Existing Solutions Hardness Experimental Studies Summary Weighted Database Graph G ( V , E , W ) Edge Weight W Node set V Edge weight w e (( v , u )) = Nodes - tuples in database, log 2 (1 + max { d v , d u } ) | V | = n ( d x - degree of node x ) The lower, the tighter Edge set E Intuition: the relationship Edges - foreign key references between one node and the between tuples, | E | = m others is distributed Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Introduction Parameterized Solution Model Existing Solutions Hardness Experimental Studies Summary Weighted Database Graph G ( V , E , W ) Edge Weight W Node set V Edge weight w e (( v , u )) = Nodes - tuples in database, log 2 (1 + max { d v , d u } ) | V | = n ( d x - degree of node x ) The lower, the tighter Edge set E Intuition: the relationship Edges - foreign key references between one node and the between tuples, | E | = m others is distributed Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Introduction Parameterized Solution Model Existing Solutions Hardness Experimental Studies Summary Weighted Database Graph G ( V , E , W ) Edge Weight W Node set V Edge weight w e (( v , u )) = Nodes - tuples in database, log 2 (1 + max { d v , d u } ) | V | = n ( d x - degree of node x ) The lower, the tighter Edge set E Intuition: the relationship Edges - foreign key references between one node and the between tuples, | E | = m others is distributed Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Introduction Parameterized Solution Model Existing Solutions Hardness Experimental Studies Summary Query and Answer Query l keywords p 1 , p 2 , · · · , p l or l subsets V 1 , V 2 , · · · , V l ⊆ V ( V i contains keyword p i ) Answer Connected subtree T in G containing the l keywords or Group Steiner tree T , s.t. V ( T ) ∩ V i � = ∅ ( i = 1 , · · · , l ) Objective Cost of answer T : s ( T ) = � ( u , v ) ∈ E ( T ) w e (( u , v )) (linear combination of node/edge weight) Output answers T 1 , · · · , T k , with top- k minimum costs (Top- k ) Minimum Group Steiner Tree Problem Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Introduction Parameterized Solution Model Existing Solutions Hardness Experimental Studies Summary Query and Answer Query l keywords p 1 , p 2 , · · · , p l or l subsets V 1 , V 2 , · · · , V l ⊆ V ( V i contains keyword p i ) Answer Connected subtree T in G containing the l keywords or Group Steiner tree T , s.t. V ( T ) ∩ V i � = ∅ ( i = 1 , · · · , l ) Objective Cost of answer T : s ( T ) = � ( u , v ) ∈ E ( T ) w e (( u , v )) (linear combination of node/edge weight) Output answers T 1 , · · · , T k , with top- k minimum costs (Top- k ) Minimum Group Steiner Tree Problem Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Introduction Parameterized Solution Model Existing Solutions Hardness Experimental Studies Summary Example Database Database Graph Author Paper−Author Paper c1 c2 c3 c4 AID Name PID Title PID AID a1 Jim 1.6 2 t1 t2 a1 1.6 Keyword Search on RDBMS 1.6 2 1.6 2 1.6 a2 Robin t2 a1 Steiner Problem in DB t4 t1 t2 t3 t4 t5 t6 t7 Citation t3 t3 a2 Efficient IR−Query over DB 2 2 1.6 2 1.6 1.6 1.6 Cite Cited t4 t4 a2 Online Cluster Problems w1 w2 w3 w4 w5 w6 w7 t1 t2 t5 t5 a2 Keyword Query over Web 2.6 2.6 2.6 1.6 2.6 t3 t2 1.6 2.6 t6 a2 t6 Query Optimization on DB t5 t4 a2 a1 a2 t7 t7 Parameterized Complexity t6 t7 Query Keyword ( p 1 ), Query ( p 2 ), DB ( p 3 ), and Jim ( p 4 ) Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Introduction Parameterized Solution Model Existing Solutions Hardness Experimental Studies Summary Example Database Database Graph Author Paper−Author Paper c1 c2 c3 c4 AID Name PID Title PID AID a1 Jim 1.6 2 t1 t2 a1 1.6 Keyword Search on RDBMS 1.6 2 1.6 2 1.6 a2 {p1} Robin t2 a1 Steiner Problem in DB t4 t1 t2 t3 t4 t5 t6 t7 Citation {p1} t3 t3 a2 Efficient IR−Query over DB 2 2 1.6 2 1.6 1.6 1.6 Cite Cited t4 t4 a2 Online Cluster Problems w1 w2 w3 w4 w5 w6 w7 t1 t2 t5 t5 a2 Keyword Query over Web 2.6 2.6 2.6 1.6 2.6 t3 t2 1.6 2.6 t6 a2 t6 Query Optimization on DB t5 t4 a2 a1 a2 t7 t7 Parameterized Complexity t6 t7 Query Keyword ( p 1 ), Query ( p 2 ), DB ( p 3 ), and Jim ( p 4 ) Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Introduction Parameterized Solution Model Existing Solutions Hardness Experimental Studies Summary Example Database Database Graph Author Paper−Author Paper c1 c2 c3 c4 AID Name PID Title PID AID a1 Jim 1.6 2 t1 t2 a1 1.6 Keyword Search on RDBMS 1.6 2 1.6 2 1.6 a2 {p2} {p1,p2} Robin t2 a1 Steiner Problem in DB t4 t1 t2 t3 t4 t5 t6 t7 Citation {p2} {p1} t3 t3 a2 Efficient IR−Query over DB 2 2 1.6 2 1.6 1.6 1.6 Cite Cited t4 t4 a2 Online Cluster Problems w1 w2 w3 w4 w5 w6 w7 t1 t2 t5 t5 a2 Keyword Query over Web 2.6 2.6 2.6 1.6 2.6 t3 t2 1.6 2.6 t6 a2 t6 Query Optimization on DB t5 t4 a2 a1 a2 t7 t7 Parameterized Complexity t6 t7 Query Keyword ( p 1 ), Query ( p 2 ), DB ( p 3 ), and Jim ( p 4 ) Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases

Introduction Parameterized Solution Model Existing Solutions Hardness Experimental Studies Summary Example Database Database Graph Author Paper−Author Paper c1 c2 c3 c4 AID Name PID Title PID AID a1 Jim 1.6 2 t1 t2 a1 1.6 Keyword Search on RDBMS 1.6 2 1.6 2 1.6 a2 {p2} {p1,p2} Robin t2 a1 Steiner Problem in DB t4 t1 t2 t3 t4 t5 t6 t7 Citation {p2,p3} {p1,p3} {p3} t3 t3 a2 Efficient IR−Query over DB 2 2 1.6 2 1.6 1.6 1.6 Cite Cited t4 t4 a2 Online Cluster Problems w1 w2 w3 w4 w5 w6 w7 t1 t2 t5 t5 a2 Keyword Query over Web 2.6 2.6 2.6 1.6 2.6 t3 t2 1.6 2.6 t6 a2 t6 Query Optimization on DB t5 t4 a2 a1 a2 t7 t7 Parameterized Complexity t6 t7 Query Keyword ( p 1 ), Query ( p 2 ), DB ( p 3 ), and Jim ( p 4 ) Ding, Yu, Wang, Qin, Zhang, Lin Finding Top-k Min-Cost Connected Trees in Databases