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

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

Our Motivation: Recent database applications on the web

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”.

Web Resources: DBLP Bibliography and SIGMOD Anthology

Data Model (by Data Provider)

Topics

Tid TName TType TDomain TImp

T01 Edward F. Codd Researcher Database 0.9

T08 data models database mngement ResearchPaper Database 0.8

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)

Edward F. Codd, “Data Models in Database Management”, 1980

“T08 is a research paper of T01”

Recursive Metalinks: RelatedToPapers, PrerequisitePapers

Topic Sources (web documents)

Relationships (Metalinks)

MId MType AntecedentId ConsequentId

M01 ResearchPaperOf T01 T08

Data Model

Topics

Query (top-k, approximate text similarity)

Use the advice at www.expert.com/advice. Find the 20 most-important papers

having 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.

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 *

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

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

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

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.

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

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

select M.ConsequentIdusing advice at www.expert.com/advice as database DBfrom DB.Topics T, DB.Metalinks Mwhere T.TType=”Index Term” and M.MType=”IndexedBy” and T.TId is-in M.AntecedentId and

T.TName (0.9) ”join algorithms”propagate importance as product function of Tstop after 20 most important

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.

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)

STOP AFTER (20) ΠConsequentId ORDER BYImportance L L.TId in R.AntecedentId

IndexedBy"" MTypeσ

*TName (0.9) “join algorithms” and TType=”Index Term”,

fout=fin*sim(TName,”join algorithms”), = 0.0 DB.Topics DB.Metalinks

Logical Query Tree

20 most-important papershaving index terms with similarity to “join algorithms” above 0.9

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.

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.ConsequentIdusing advice at www.expert.com/advice as database DBfrom DB.Topics T, DB.Metalinks Mwhere TType = ”Index Term” and M.MType = ”ResearchTopicOf” and T.Td is-in M.AntecedentId and T.TName (0.9) “join algorithms”propagate importance as gmtrc-average function of T, Mstop after 5 most important

STOP AFTER (5) ConsequentId ORDER BYImportance * L.TId in R.AntecedentId, fout=sqrt(flin*frin), = 5

*TName (0.9) “join algorithms” picOf"ResearchTo" MTypeσ

and TType=”Index Term”, fout=fin*sim(TName,”join algorithms”), = 0.0 DB.Topics DB.Metalinks

Semantics of TClosure

FPath:

X.

.

.

.

tP1 Pn

. . .

FPathMerge

Metalink types have associated axioms Ex. RelatedTo is transitive and reflexive

SubTopicOf is 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.

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

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

risj

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 vector fS = <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

Evaluation of SVA TClosure Operator

• Compute Topic Closure X+ where regular expression R is a single metalink type M

• Each metalink VM 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

• 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.

0.8 RelatedTo 0.6 0.85 0.9 Pre 0..95 0.7 Pre Pre 0.9 0.95 0.9

T2

T333

T4

T111

T5

MType Tid1 Imp(Tid1) ParentListChildList

<Tid2, Imp(Tid2), Imp(Mid)> triplets

Pre T1 0.9 {} <T3,0.85,0.95>, <T4,0.95,0.9>

Pre T3 0.85 {T1} -

Pre H1 Avg(0.9, 0.95) = 0.925

{T3, T4} <T5,0.7,0.9>

RelatedTo T1 0.9 {T2, T3, T4} <T2,0.8,0.6>,<T3,0.85, 0.95>, <T4,0.95,0.9>

Tid NodeList <TidList, Hid>

T3 <{T3,T4}, H1>

T4 <{T3,T4}, H1>

MIndex HIndex

Example 5.

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.

Experimental Results SVA 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.

Tuple Comparisons

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NLoopSVTNLoopSimSVT

Tuple Comparisons

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Top-k

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NLoopTopK

NLoopSimTopK

Experimental Results SVA 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.

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Sideway Values Threshold [0,1]

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Sideway Values Threshold [0,1]

defualtMetalinks/topic R=7Topics and Metalinks have Imp[0.7,1.0] Buffer Size=1000Input Size=500

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Topics and Metalinkshave Imp[0.7,1.0] Input Size=500

Conclusions

• Sideway Values and Functions

• SQL Extensions and SVA

• Application: Web Querying