aggregate queries in peer-to-peer olap
DESCRIPTION
Aggregate Queries in Peer-to-Peer OLAP. Mauricio Minuto Espil Faculty of Engineering Universidad Católica Argentina Alejandro A. Vaisman Computer Science Department Universidad de Buenos Aires. 7 th International Workshop on Data Warehousing & OLAP. - PowerPoint PPT PresentationTRANSCRIPT
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Aggregate Queries Aggregate Queries in Peer-to-Peer OLAPin Peer-to-Peer OLAP
• Mauricio Minuto Espil Faculty of Engineering Universidad Católica Argentina• Alejandro A. Vaisman Computer Science Department Universidad de Buenos Aires
7th InternationalWorkshop on
Data Warehousing &OLAP
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OUTLINE:
• CHARACTERIZATION• PROBLEM AND PROPOSAL• FACT INTEGRATION• DIMENSION INTEGRATION • AGGREGATE QUERIES• CONCLUSIONS
Aggregate Queries Aggregate Queries in Peer-to-Peer OLAPin Peer-to-Peer OLAP
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Peer-to-Peer Systems
Involves a network of interconnected peer systems;The network topology is not relevant;Each peer maintains full autonomy over its own data resources; Each peer may assume the role of local. The rest become acquaintances of the local peer;The roles of local and acquaintance among peers are not static; they are functional and are determined with respect to an operation.
MAIN CHARACTERISTICS:
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Peer-to-Peer Data Management
No global schema is assumed to exist for data; Each peer must manage its data according its own perspective;A query may be posed on any peer, the responsive peer becomes local with respect to the query;Answers to queries must conform the best attempt to gather data from all peers; Answers to queries posed by local peer users must conform the view those users have of their data;Peers must cooperate in maintaining the local views of data;
MAIN CHARACTERISTICS:
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OUTLINE:
• CHARACTERIZATION• PROBLEM AND PROPOSAL• FACT INTEGRATION• DIMENSION INTEGRATION • AGGREGATE QUERIES• CONCLUSIONS
Aggregate Queries Aggregate Queries in Peer-to-Peer OLAPin Peer-to-Peer OLAP
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OLAP Data in a Peer-to-Peer System
• OLAP data is essentially multidimensional;• Multidimensional data consists in a collection of views of base and derived aggregated data, describing fact indicators by dimensions of analysis; • Concepts for aggregation within dimensions are obtained from finer grain concepts through hierarchies;• Different peers may have affine fact indicators described by different dimension hierarchies;• Integration is needed: Any summary concept that appears in a hierarchy of a peer acquaintance must be transformed into a summary concept meaningful to the local peer. •••• >
THE PROBLEM:
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OLAP Data in a Peer-to-Peer System
• The expected integration is not always possible;• Users may pose OLAP queries in a local peer expecting results involving all relevant data stored in all peers.• Local queries must be propagated among the acquaintances;• A rewriting of the propagated queries is needed to conform the view of the local user.• The rewriting technique must accomplish the data integration on the fly;• Incomplete and uncertain results must be admitted;
•••• > THE PROBLEM
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Peer-to-Peer OLAP
• FACT PEERS• DIMENSION PEERS• AGGREGATE P2P OLAP QUERIES• COMPLETE AND CERTAIN QUERY ANSWERS
MODEL (DEFINES):
• AUTONOMOUS PEER DATA MANAGEMENT• THREE PHASE PEER TO PEER COORDINATION• COOPERATIVE QUERY ANSWERING
ARCHITECTURE (INVOLVES):
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OUTLINE:
• CHARACTERIZATION• PROBLEM AND PROPOSAL• FACT INTEGRATION• DIMENSION INTEGRATION • AGGREGATE QUERIES • CONCLUSIONS
Aggregate Queries Aggregate Queries in Peer-to-Peer OLAPin Peer-to-Peer OLAP
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Fact Integration
• GENERIC FACT • FACT PEERS
TYPES OF FACT:
IS-A RELATIONSHIP
FACT CONCILIATION PHASE:
SOURCE PEER
PUBLISHES GENERIC FACT DEFINITION AND DIMENSIONAL STRUCTURE
LISTENING PEER
GENERIC FACT AGREEMENT AND DIMENSION PEERS DEFINITION
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OUTLINE:
• CHARACTERIZATION• PROBLEM AND PROPOSAL• FACT INTEGRATION• DIMENSION INTEGRATION• AGGREGATE QUERIES• CONCLUSIONS
Aggregate Queries Aggregate Queries in Peer-to-Peer OLAPin Peer-to-Peer OLAP
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Dimension Integration
• LEVEL HIERARCHY INTEGRATION• MEMBER HIERARCHY INTEGRATION.
CONSISTS IN:
• CORRESPONDENCE DEFINITION AMONG DIMENSION LEVELS • REVISION/MAPPING DEFINITION AMONG DIMENSION INSTANCES
COMPRISES:
INVOLVES:• A PAIR OF DIMENSION PEERS
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Level Hierarchy Integration
LEVEL CORRESPONDENCE• APPLIES ON SCHEMAS• ESTABLISHES HOW A PAIR OF LEVELS ON DIFFERENT PEER DIMENSIONS ARE RELATED• IS PRODUCED/UPDATED DURING A SCHEMA CONCILIATION PHASE• IS MATERIALIZED AS METADATA IN CORRESPONDENCE TABLES
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ORDER PRESERVING LEVEL CORRESPONDENCE
Benefit Type
Funding Class
All
Tax DischargeCategory
Loan Type
All
Charity Modality
BenefitType
Level Hierarchy Integration
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A LEVEL CORRESPONDENCE THAT DO NOT PRESERVE ORDER IS NOT ADMISSIBLE
Benefit Type
Funding Class
All
Tax DischargeCategory
Loan Types
All
Charity Modality
BenefitType
Level Hierarchy Integration
WRONG
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Member Hierarchy Integration
INTEGRATION BY MAPPING
• APPLIES ON INSTANCES• ESTABLISHES HOW A PAIR OF MEMBERS OF CORRESPONDING LEVELS ARE RELATED• IS PRODUCED/UPDATED DURING A MAPPING ACQUISITION PHASE• MUST BE PRECEDED BY AT LEAST ONE SCHEMA CONCILIATION PHASE• IS MATERIALIZED AS METADATA IN MAPPING TABLES
l1: m1 (Local) l'1: m'1 (Peer)
l2: m2 (Local) l'2: m'2 (Acq)
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For each member m of a level l, such that map (l:m) is defined,
if there exists some member m’ of level l’, satisfying roll-up (l:m) = l’:m’
and level l’ is in dom(Correspondence)then roll-up (map (l:m) ) = map (l’:m’).
Member Hierarchy Integration
MAPPINGS: HOMOMORPHISM PROPERTY
l:m
l':m’map
maproll-uproll-up
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Member m’ in level l’ is conflicting,it cannot be mapped.
An approach based on mapping exclusively is not always effective.
Member Hierarchy Integration
HOMOMORPHISM MAY NOT BE ALWAYS GRANTED
l:m1
l':m’
mapmap
roll-uproll-up
l:m2
roll-uproll-up
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MAPPINGS DO NOT SUFFICE: MAPPINGS DO NOT SUFFICE: REVISIONS MAY BE NECESSARYREVISIONS MAY BE NECESSARY
Member Hierarchy Integration
l:m1
l':m’
l:m2
Conflicting Member
REVISIONS AFFECT THE VIEW A PEER HAS OF THE REVISIONS AFFECT THE VIEW A PEER HAS OF THE HIERARCHY OF ITS ACQUAINTANCE ONLYHIERARCHY OF ITS ACQUAINTANCE ONLY
LOCAL
ACQUAINTANCE
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A REVISION BY SPLITTING A REVISION BY SPLITTING MAY BE USED TO REPAIR CONFLICTSMAY BE USED TO REPAIR CONFLICTSGIVING WAY TO MAPPABLE MEMBERSGIVING WAY TO MAPPABLE MEMBERS
Member Hierarchy Integration
l:m1
l':m2’
l:m2
l:m1’
LOCAL
ACQUAINTANCE
EXAMPLE OF A REVISION: EXAMPLE OF A REVISION: CONFLICTING MEMBER SPLITCONFLICTING MEMBER SPLIT
Non-Conflicting Members
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A REVISION BY RECLASSIFYING A REVISION BY RECLASSIFYING MAY BE AN ALTERNATIVE TO RESTORE HOMOMORPHISMMAY BE AN ALTERNATIVE TO RESTORE HOMOMORPHISM
Member Hierarchy Integration
l:m1
l:m2
l:m’
LOCAL
ACQUAINTANCE
l:m3
l':m”
EXAMPLE OF A REVISION:EXAMPLE OF A REVISION:CONFLICTING MEMBER RECLASSIFICATIONCONFLICTING MEMBER RECLASSIFICATION
Non-Conflicting Members
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• PRODUCES AND BROADCASTS REVISION AND MAPPING DEFINITIONS TO POTENTIAL ACQUAINTANCES
REVISE AND MAP APPROACH:LOCAL PEER:
Member Hierarchy Integration
ACQUAINTANCE:• REVISES ITS OWN HIERARCHIES PRODUCING A REVISED INSTANCE (REVISED ROLL-UPS) WITH RESPECT TO THE LOCAL PEER• STORE INFORMATION ON MAPPINGS IN METADATA MAPPING TABLES
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Whenever some member m2’ of a level l’ is not mapped,a bottom-up completion approach for query answeringis employed: information on non-mapped members andtheir roll-ups is stored in metadata completion tables.
Member Hierarchy Integration
BOTTOM-UP COMPLETION APPROACH
l:m1
l':m2’
mapmap
Incompleteroll-up
roll-upl:m2
roll-uproll-up
l':m1’Non-Mapped
Member
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OUTLINE:
• CHARACTERIZATION• PROBLEM AND PROPOSAL• FACT INTEGRATION• DIMENSION INTEGRATION• AGGREGATE QUERIES• CONCLUSIONS
Aggregate Queries Aggregate Queries in Peer-to-Peer OLAPin Peer-to-Peer OLAP
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P2P OLAP Queries
Syntactical Structure (Datalog Style):
query( Z1, ... , Zn, aggr(M), Set of Peers) Generic Fact(X1, ... , Xn, M ), rollup dimension d1 from bottom level to desired level l1 ( X1, Z1 ), ... , rollup dimension dn from bottom level to desired level ln ( Xn, Zn );
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• GENERATES A QUERY FOR EACH RELEVANT PEER (INCLUDING THE LOCAL PEER);• GENERATED QUERIES ARE PROPAGATED TO RELEVANT PEERS;• QUERIES FOR RELEVANT PEERS STEM FROM THE REWRITING OF THE SUBMITTED P2P OLAP QUERY;• THE REWRITING PROCESS INTRODUCES REFERENCES TO FACT PEERS, REVISED ROLL-UPS, AND MAPPING AND COMPLETION TABLES;• RESULTS OF PROPAGATED QUERIES ARE COLLECTED AND AGGREGATED LOCALLY TO PRODUCE THE FINAL QUERY ANSWER;• QUERY ANSWERS MAY BE UNCERTAIN AND INCOMPLETE DUE TO BOTTOM-UP COMPLETION.
Query Evaluation Process
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Query ProcessingQuery Processing
Local Peer Relevant Peer
Fact Fact tablestables
QUERY
Rewriting
Evaluation
Partial Result
Revised Revised RollupsRollups
MetadataMapping Mapping
tablestables
IntegrationAnswer
Completion Completion tablestables
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Aggregate Queries Aggregate Queries in Peer-to-Peer OLAPin Peer-to-Peer OLAP
• GENERIC FACTS• FACT CONCILIATION PHASE• HIERARCHY LEVEL CORRESPONDENCE• SCHEMA CONCILIATION PHASE• REVISE AND MAP APPROACH• BOTTOM-UP COMPLETION• MAPPING ACQUISITION PHASE• P2P OLAP QUERIES• QUERY REWRITING AND EVALUATION
CONCLUSIONS: MAIN POINTS DISCUSSED