business intelligence on complex graph data dritan bleco yannis kotidis ([email protected])...
TRANSCRIPT
Business Intelligence on Complex Graph Data
Dritan Bleco Yannis Kotidis ([email protected]) ([email protected])
Department of InformaticsAthens University Of Economics and Business
BEWEB 2012Berlin
Dritan Bleco
Outline•Motivation•Graph Data Model•Operators on Graph Data•Querying Graph Records•Query Rewrites• Experiments•Conclusions
Motivational Example• A Supply Chain Management (SCM) application
• Tracks the different routes that articles of a customer order follows from production lines to the consumer hands
• Multiple warehouses are located among the production lines and the shipping points and can stage the products while the order is being assembled
• RFID readers are used to keep track of the location of the articles
• An order follows one or more paths so our web supply chain application produces graph like data
Dritan Bleco
A :1
D :8 F
B
G
HStart Node End Node MeasureA B 15A C 11
C E 7B E 5B D 9E E 8
E
E D 4E F 2C G 43D H 6
Node Location
A Thessaloniki
C Trikala
B Lamia
D Athens
E Athens
F Athens
G Iraklion
H Kalamata
F G 9F H 4
C
C C 1
Production Lines
Warehouses
Shipping Points
11
155
9
72
4
43
9
4
6
Dritan Bleco
AC:1
D
:8 FB
G
H
E
Node Location
A Thessaloniki
C Trikala
B Lamia
D Athens
E Athens
F Athens
G Iraklion
H Kalamata
11
15
43
7
5
9
29
4
6
Q1: What is the total order completion time?
The longest path between nodes A and G,H
Q2: What is the total processing time for parts that are shipped through warehouses located in Athens?
The longest path between nodes A and G,H considering only paths that transverse at least one location in Athens.
4
Dritan Bleco
AC:1
D
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
U
Aggregate Nodes
Aggregate Node U coalesces Warehouses located in Athens
Set In(U) contains the set of nodes of U that have at least one incoming edge from nodes that do not belong U: In(U)={D, E}
Set Out(u) contains nodes in U that have at least one outgoing edge towards a node that does not belong to U: Out(U)={D,F}
A single node can be abstracted as an aggregate node whose internal structure is not revealed to the query: E =[in(E) ,out(E)] :8 Dritan Bleco
AD
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
PathC:1
Different simple Paths
Dritan Bleco
C:111
7
(ACE) starting from out(A) end ending to in(E) (internal measure 8 is not included)
(ACE] starting from out(A) end ending to out(E) (internal measure 8 is included)
(AE)
E:8
(AE]
AD
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
Node
C:1
Different simple Paths
Dritan Bleco
(ACE) starting from out(A) end ending to in(E) (internal measure 8 is not included)
(ACE] starting from out(A) end ending to out(E) (internal measure 8 is included)
Starting from in(E) end ending to out(E) [in(E),out(E)]= E
E - Path [EE]
E:8
AD
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
Composite Path [AE]*C:1
Composite Paths: Paths with same Starting and Ending Node
[A,E]* ={ [ACE], [ABE] }
Dritan Bleco
A
C:1
E:8
B
11
7
515
AD
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
U
Composite Path [A in(u))*
C:1
Composite Paths: Paths with same Starting and Ending Node
[A,E]* ={ [ACE], [ABE] }
[A, in(U))* ={ [ACE),[ABE),[ABD)}
Dritan Bleco
A
C:1
B
11
7
515 9
AD
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
U
Composite Path [in(U)out(U)]*
C:1
Composite Paths: Paths with same Starting and Ending Node
[A,E]* ={ [ACE], [ABE] }
[A, in(U))* ={ [ACE),[ABE),[ABD)}
[in(U),out(U)]* ={ [EF],[ED] }
Dritan Bleco
FE:8
D
2
4
AD
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
Operators on Graph DataC:1
Path-join operator concatenates two paths p1 and p2
1. Ending node of p1 is the same as the starting node of p2 2. One of the two paths is open-ended at the common end-point.
[ACE) [EFG]= [ACEFG]
Dritan Bleco
A
C:1
E:8 FG11
7 29
AD
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
U
Operators on Graph DataC:1
Path-join operator concatenates two paths p1 and p2
1. Ending node of p1 is the same as the starting node of p2 2. One of the two paths is open-ended at the common end-point.
[ACE) [EFG]= [ACEFG]
[Pr, in(U)) [in(U), out(U)] (out(U), Sr]
Pr
Sr
Dritan Bleco
A
C:1
E:8 F
D
11
7 2
415 B
59
G
H
9
46
AD
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
Operators on Graph DataC:1
πp(r) Path projection operator projects the record on the edges defined in path p, while retaining their measures.
Π[ACE)(r)={(A,C):11, (C,C):1, (C,E):7 }
Dritan Bleco
A
C:111
7
15 B5
9
The projection of a record on a composite path is computed as a set containing the projections into the constituent paths.
Π[AE)*(r)={ {(A,C):11, (C,C):1, (C,E):7 } , {(A,B):15, (B,E):5 } }
AD
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
U
BI on Graph DataC:1
Intra-Path Aggregate Function Fp(r) : applied on the measures resulting from the projection of record r on path p Sum[ACE)(r)=[ACE):19 Sum[AE)*(r)={ [ACE):19 , [ABE):20}
Pr
Sr
Inter-Path Aggregate Function G(Fp(r) ): consolidates the result(s) obtained via Inter- Path aggregation.
Max(Sum[ACE)*(r) )=Max({ [ACE):19, [ABE):20 })=[ABE):20
Max(Sum[Pr, Sr]*(r)) returns the order completion time for the order depicted in record rDritan Bleco
[ABE):20
[ACE):19
AD
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
U
Queries using operatorsC:1
Pr
Sr
Dritan Bleco
AD
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
U
Query RewriteC:1
Pr
Sr
Dritan Bleco
A
C:1
E:8 F
DB
G
H
ΜΑΧ( SUM[Pr, in(U)) [in(U), out(U)] (out(U, Sr] (r)) =
MAX (SUM[Pr, in(U))(r) SUM SUM[in(U), out(U)] (r) SUMSUM(out(U, Sr] (r))
Generally G(Fp=p1 p2 (r)) = G ( Fp1(r) H Fp2(r) ) : pushing intra-path on a path
AD
:8 FB
G
H
E
11
15
43
7
5
9
29
4
6
4
U
Query RewriteC:1
Pr
Sr
Dritan Bleco
A
C:1
E:8 F
DB
G
H
ΜΑΧ( SUM[Pr, in(U)) [in(U), out(U)] (out(U, Sr] (r)) =
MAX (SUM[Pr, in(U))(r) SUM SUM[in(U), out(U)] (r) SUMSUM(out(U, Sr] (r))
MAX ({[ABE):20 ,[ACE):19,[ABD):24} SUM{ [EF] :10,[ED]:12,[DD]:0} SUM{ (FG] :9, (FH]:4, (DH]:6})
MAX( {[ABEFG]:39, [ACEFG]:38, [ABEFH]:34, [ACEFH]:33, [ABEDH]:38, [ABEDH]:37 [ABDH]:30} ) = [ABEFG]:39
[ACE):19 [ABE):20
[ABD):24
[EF]:10[ED]:12[DD]:0
(FG]:9
(FH]:4(DH]:6
Experiments (I)• Two real Schema Graphs:
1. * BAY: Depicts San Francisco Bay Area roads and
2. **Gnutella: Describes connections among Gnutella hosts from August 2002.
• 120 million records are synthesized and assigned random real values to the labels of each record.
• Experimental evaluation using the PBS (Pick By Size)
• Queries 50% intra-path and 50% inter-path chosen with zipf or unif.
• Independent evaluation of the Cost via the total number of tuples that need to be retrieved
• * http://www.dis.uniroma1.it/~challenge9/download.shtml• ** http://snap.stanford.edu/data/p2p-Gnutella05.html
Experiments (II)
PBS, Bay Data Set, Uniform 100 Queries PBS, Bay Data Set, Zipf 100 Queries
PBS-1 considers only intra-path materialized aggregates
PBS-2 considers only inter-path materialized aggregates
PBS selects and materializes both types of views depending on the query workload
Dritan Bleco
Experiments (III)
PBS, Gnutella Data Set, Uniform 100 Queries PBS, Gnutella Data Set, Zipf 100 Queries
PBS-1 considers only intra-path materialized aggregates
PBS-2 considers only inter-path materialized aggregates
PBS selects and materializes both types of views depending on the query workload
Dritan Bleco
Experiments (IV)
Varying Query Mix, BAY Data Set, Uniform Queries
Varying Query Mix, BAY Data Set, Zipf Queries
Mix of intra-/inter-path queries in the BAY dataset for a fixed budget of 20%.
For inter-paths queries PBS and PBS-2 have the same performance
For only intra-path queries PBS-1 and PBS give the best performance.
PBS that considers both types of views provides consistently the largest reduction in query cost. Dritan Bleco
Conclusions• A framework for modeling analytical queries in a graph
database independent of the • underlying storage representation of the records • the query language used
• Our framework • Permits rewriting of complex aggregations into smaller
computational units• Enables cost-based query optimization and pre-
computation of frequently used calculations.
• Experimental results show that proper selection of materialized views can provide substantial gains in a large data warehouse containing millions of graph records.
Dritan Bleco
Thank you,
Questions?
Dritan Bleco