Sideway Value Algebra for Object-Relational Databases

1. Sideway Value Algebra for Object-Relational Databases G. Ozsoyoglu A. Al-Hamdani I. S. Altıngovde S.A. Ozel O. Ulusoy Z.M. Ozsoyoglu Case Western Reserve University, USA Bilkent University, Turkey

2. Our Motivation: Recent database applications on the web Attach (a) Functions to relations “Sideway Value Fncts” (b) Function evaluations to tuples of relations “Sideway Values” “Scores” :Cohen, Sigmod’98 “Preference values” : Agrawal and Wimmers, Sigmod’00 Hristidis, Papakonstantinou, Koudas, Sigmod’01 “Probabilistic values”: Barbara, Garcia-Molina, Porter, IEEE TKDE’92

3. Sideway Values and Functions Represent • Recommendations of Data Creators, • Preferences of users.Importance Values Employed for • User-guided query output ranking, • Top-K “query evaluation”. Integrated with “approximate text joins”.

4. Web Resources: DBLP Bibliography and SIGMOD Anthology Data Model (by Data Provider) Topics Edward F. Codd, “Data Models in Database Management”, 1980 Query: Database Researchers with a name similar to E. Codd?Text similarity between Edward F. Codd and E. Codd is judged to be 0.7 Result: Tuple T01 is returned with importance value 0.63 (0.9 * 0.7)

5. Data Model Topics Relationships (Metalinks) “T08 is a research paper of T01” Recursive Metalinks: RelatedToPapers, PrerequisitePapers Topic Sources (web documents)

6. Query (top-k, approximate text similarity) Use the advice at www.expert.com/advice. Find the 20 most-important papershaving index terms with similarity to “join algorithms” above 0.9 Query (time constraints, topic closure, threshold ) Use the advice at www.expert.com/advice . Find in two minutes those Anthology papers that are prerequisites of T08 with importance values above 0.7.

7. Summary So Far • Importance values as sideway values/functions • Top-k or threshold-based queries • Regular-expression-based topic closure queries:PapersWrittenBy(RelatedToPapers*(T08)) • Expensive metalink importance value computation *RelatedToPapers, PrerequisitePapers • Time Constraints *

8. Rest of the talk • SQL extensions for sideway values • Sideway Value Algebra (SVA) operators for Selection Join Topic Closure • Evaluations of SVA operators Join Topic Closure • Experimental results

9. SVA queries propagate sideway values to output relations in automated ways.Query output sizes controlled by(a) Ranking threshold k (final output size control) (b) Sideway value threshold Vt (intermediate output size control)(c) k and Vt

10. SVs attached to base relations • Open Form:SV stored in column of base relation. • Closed Form:SV derived thru closed function. Ex: for relation Employee, we have Imp (Salary,JobCode) = a.Salary + b.JobCode • Semi-Closed Form:SV value for a set of tuples identified through regular expression. Ex: Imp(<TopicName = “*kidney complications*”>) = 0.9

11. Approximate Text Similarity • Vector space based similarity model. • Vocabulary W for all words (terms). • Represent each topic as a vector of |W| terms. • TF-IDF model of IR, and cosine similarity.

12. SQL Extensions • Database using advice at www.xx as database • Propagate Sideway Values propagate importance as <type> function of <arg list> • Stopping Conditions stop after k stop with threshold Vt stop after k and with threshold Vt

13. 20 highest topic-importance-ranked papers having index terms with similarity to “join algorithms” above 0.9. A product-based importance propagation function. IndexedBy: SetOf IndexTermId  PaperId selectM.ConsequentId using adviceatwww.expert.com/adviceasdatabaseDB from DB.Topics T, DB.Metalinks M whereT.TType=”Index Term” and M.MType=”IndexedBy” and T.TIdis-in M.AntecedentId and T.TName (0.9) ”join algorithms” propagate importance asproductfunction ofT stop after 20 most important

14. SVA Operators For each RA operator, there is SVA counterpart extended with (a) Output SV function fout (b) Output threshold  (ranking or sideway threshold )  Operators with superscript * : SVA operators.  Operators without superscript * : RA operators. They carry sideway values of the left or right relation.

15. SVA Selection: σ*C, fout, (R) Input • Input relation R with sideway function fin • Selection Condition C • Output sideway propagation function fout • Output threshold  (k or Vt) Output =k : Top-k fout-ranking tuples that satisfy C =Vt : Tuples with fout value greater than Vt and satisfy C  = (k,Vt)

16. 20 most-important papershaving index terms with similarity to “join algorithms” above 0.9 Logical Query Tree

17. SVA Join: L *A  B, fout,  R Input • L and R with two functions flin and frin • Join Condition  on attributes A and B • Output sideway propagation function fout • Output threshold  (k or Vt) Output: join of L and R Sideway values of output tuples computed by fout. Output threshold  satisfied.

18. Query: Five researchers with (a) papers having index terms similar to “join algorithms” above 0.9 (b) geometric averages of highest importance values.ResearchTopicOf: SetOf Index-termId  ResearcherId select M.ConsequentId using advice at www.expert.com/advice as databaseDB fromDB.Topics T, DB.Metalinks M where TType = ”Index Term” and M.MType = ”ResearchTopicOf” and T.Td is-inM.AntecedentId and T.TName (0.9) “join algorithms” propagate importance asgmtrc-averagefunction ofT, M stop after5most important

20. Semantics of TClosure X . . . . Pn P1 FPath: t . . . FPathMerge

21. Metalink types have associated axioms Ex.RelatedTo is transitive and reflexive SubTopicOfis transitive but not reflexive Computing topic closure requires • Sound and complete set of axioms for metalink types, and • Polynomial-time algorithm to compute the topic closure using the axioms.

22. Evaluation of SVA Join Operator • Nested-Loops-Based algorithms for top-k-based and sideway-value-based threshold Join operators • Sorted input relations wrpt sideway values. • fout() function is monotone e.g. Product, numeric average, geometric average

23. Nested-Loops Threshold Join Algorithm • Enforce new stopping conditions while processing inner and outer loops. • Inner loop (S) exits: fout() value of the tuple ri*sj < Vt (ri is in R and sj is in S). • Outer loop (R) exits at the ith iteration: fout() value of the output tuple ri.s1 < Vt (ri is in R and s1 is the first tuple in S) R S ri sj

24. Nested-Loops Threshold Join Algorithm with Approximate Text Match Join Conditions • Similarity of text-valued join attributes > threshold tsim • Use vector-space model. • Term vector ur = <u1 u2 … ux> corresponding to join attribute A of tuple r in R, where ui represents weight of term i in A • Filter vectorfS = <w1 ... wx>: each value wi is the max weight of the corresponding term i among all vectors of S • Cosine (ur, fS) : the maximal similarity of a record r in R to any other record s in S • if Cosine (ur, fS) < Vt then r can not be similar to any tuple s in S with similarity > Vt

25. Evaluation of SVA TClosure Operator • Compute Topic Closure X+ where regular expression R is a single metalink type M • Each metalink VM Tid is represented by a tuple in the Metalinks table V is a set of topic identifiers and Tid is a topic identifier • All metalinks are RHS-decomposable. • If a metalink type is LHS-decomposable then each metalink with V in LHS is decomposed into multiple metalinks with a single topic in LHS

26. Create index MIndex for all metalink instances • TClosure algorithms use only MIndex to find closure of a given set of topics. • Create a second index HIndex to maintain all nodes that are not decomposable.

27. Example 5. MIndex HIndex

28. Ranking-based Topic Closure Algorithm • First compute the initial candidate top k ranked topics from input topics X. • Then, in each iteration i, • Extract ith top-ranked topic from current k-i+1 candidate top-ranked topics, and • Update current candidate topics by processing all emanating metalinks from ith topic. • Algorithm requires k iterations in order to compute the top-k-ranked topic closure of a set X of input topics.

29. Experimental ResultsSVA Join Operator • Extracted titles of journals and conf. papers from the DBLP data set into two different files, R and S. • For arbitrary predicates and monotone SV functions, algorithms NLoopSVT and NLoopTop-k improve the performance of (block-nested loops) BNL considerably. • For similarity-based joins, the algorithms are further optimized, and more gains are obtained.

31. Experimental ResultsSVA Topic Closure Operator • Synthetically generated data for • Topics file with N, 1000 ≤ N ≤ 100,000, topics. Topic importance values in [0.4, 1.0] • Metalink file with metalinks/topics ratio of 3. Metalink importance values in [0.4, 1.0] • Set X of input topics with size= 100 topics. Topic importance values in [0.5, 1.0] • Disk-based MIndex file generated from topic and metalink files. • In-memory buffer of size 100KB. A sparse index table of size 1000 tuples.

34. Conclusions • Sideway Values and Functions • SQL Extensions and SVA • Application: Web Querying