Graph Databases: Efficient storage ? and Rapid retrieval ?

1
Graph Databases Efficient storage ? and Rapid
retrieval ?

• Robert Levinson
• Machine Intelligence Laboratory
• University of California
• Santa Cruz

2
THE CG MARS LANDER

• High level architecture

English-CG-English Translation
English Discourse
English Queries
English Translator, Source reference, GUI
CG Creator/Translator with Type Hierarchy
CG Parser Processor
Query Processor Matcher
Answer more specific CGs in DB
ADB Processor
Santa Cruz The CG Mars Lander
ADB
3
THE CG MARS LANDER
document
English
queries
CGs
TH
replies
4
SUBGRAPH-ISOMORPHISM

• NP-COMPLETE ?
• 2 Main Methods
• A. Backtracking Search
• B. Refinement O(n2) on avg. ?
• (both exploit candidate binding lists, modulo
  type hierarchy)
• Key Idea Amortize Cost Over
• Millions of Operations
• Mega-graph storage

5
Exploit Symmetry !! ?

• Invariant with respect to transformation.
• Shared information between objects
• or systems or their representations.
• ABAC A(BC). ?

6
Symmetry Synonyms

• similarity
• commonality
• structure
• mutual information
• relationship
• redundancy

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Total Information Diversity Symmetry

• Diversity corresponds to Comp Sci Complexity
  resources required.
• Diversity can often only be resolved with
  Combinatorial Search ???

8
Conceptual Graph Processing

• Concept Types a cat is an animal
• Relation Types or Graph Type
  mother-of Is parent-of
• Transitivity of Projection (subgraph-isomorphism
• Redundant Substructures
• Redundant Literals
• Redundant Pointers

9
6 Retrieval Methods

• Method I Flat Ordering
• Method II 2-Levels Indexes, Graphs
• Method III Full Partial Order Hierarchy
• Method IV Multi-Level Hierarchical Retrieval
• Method V Remember Node Bindings
• Method VI UDS The Universal Data Structure ?

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THE CG MARS LANDER

• Exploit Tuple-Based Linear CGs ! ?
• (a conceptual graph syntax
• that supports rapid retirieval and
  question-answering).

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_at_CG000

• AGNT (government, BE) .
• _at_CG001
• AGNT (Hungarian_American_Enterprise_
  Fund, invest),
• OBJ (invest, Dollars 1000000
  ),
• IN (Dollars 1000000,
  first_business)
• .
• _at_CG002
• AGNT (_at_CG000, manage),
• OBJ (manage, _at_CG001) .

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THE CG MARS LANDER

• A query
• / Q2 Does anybody own the rag newspaper
• New York Post ? /
• Query_at_bob_202
• ISA ( New_York_Post , newspaper n34861
  ) ,
• CHRC ( newspaper n34861 , rag n9
  ) ,
• AGNT ( own v9125 , ????? ) ,
• .

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THE CG MARS LANDER

• Answer ?? ?
• / A2 Rupert Murdoch once owned the troubled
  tabloid newspaper
• New York Post. /
• _at_CG1684_3
• ISA ( New_York_Post , newspaper n34861
  ) ,
• CHRC ( newspaper n34861 , tabloid
  n27111 ) ,
• CHRC ( newspaper n34861 , trouble
  n25320 ) ,
• AGNT ( own v9125 , Rupert Murdoch) ,
• CHRC ( own v9125 , once )
• .

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THE CG MARS LANDER

• Capabilities timings
• Inputs
• CGs (tens of thousands)
• pre-processed parts of speech
• Type Hierarchy (150,000 WORDNET augmented English
  words)
• natural language queries
• Outputs
• CG (save restore) DB
• replies to queries
• specializations and maximal specializations

15
THE CG MARS LANDER

• Capabilities timings
• benchmark machine
• Sun Ultra Enterprise 4000 (with 4 UltraSPARC
  167Mhz and 512KB External Cache CPU and 256MB of
  main memory)
• Read, process, and store an 18,000 CG input file
  in 1 hour and 46 minutes. ?
• Reloading of above DB takes on the order of
  seconds. ?
• A 150,000 word ontology is processed in 16
  seconds. ?
• Each query is handled in at most 5.5 seconds.?
• For smaller database (hundreds of CGs only), the
  time to handle a single query can be as low as
  0.2 seconds. ?

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THE CG MARS LANDER

• Cost/benefit analysis
• assume N CGs and Q queries
• Method I Cost
• Method III Cost
• N insertions
• Q queries

N
?
Q
N
2
N
?
log

10
2
2
Q
?
log
N
10
17
Cost/ benefit table

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THE CG MARS LANDER

• 6 UDS DESIGN PRINCIPLES
• 1. Every primitive data object, label or symbol
  should be stored only once with pointers used to
  denote the actual uses of the object.
• 2. Every compound object should be stored with
  the minimum information required to represent the
  combination of its parts.

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THE CG MARS LANDER

• 3. Given no loss of accuracy, objects should be
  processed at the highest level of abstraction
  possible.
• 4. If one were to implement a conceptual graph
  based on the diagrammatic representation, the
  costs associated with storage and matching would
  be much higher than they need to be.

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THE CG MARS LANDER

• 5. The same abstraction mechanism that goes from
  labels to graphs can be taken one step further to
  facilitate the storage and retrieval of nested
  context graphs.
• 6. A graph is itself the best descriptor of its
  nodes.

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CONCLUDING THOUGHTS

• The key to efficient implementation of CGs is the
  exploitation of symmetry or structure. ?
• CG operations can be executed efficiently in
  real-time applications. ?
• At the implementation or machine level knowledge
  representation formalisms sre often nearly the
  same. ?

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THE CG MARS LANDER

• References
• 1 C. Colin and R. Levinson, Partial order
  maintenance,'' Special Interest Group on
  Information Retrieval Forum, vol. 23, no. 3,4,
  pp. 34-59, 1988.
• 2 G. Ellis, R. A. Levinson, and P. Robinson,
  Managing complex objects in PEIRCE,'' Special
  Issue on Object-Oriented Approaches in Artificial
  Intelligence and Human-Computer Interaction
  (IJMMS), vol. 41, pp. 109-148, 1994.
• 3 R. Hughey, R. Levinson, and J. D. Roberts,
  eds., Issues in Parallel Hardware for Graph
  Retrieval, 1993.

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More references

• 4R. Levinson, A self-organizing retrieval
  system for graphs,'' in AAAI-84, pp. 203-206,
  Morgan Kaufman, 1984.
• 5 R. Levinson, Pattern associativity and the
  retrieval of semantic networks,'' Computers and
  Mathematics with Applications, vol. 23, no. 6-9,
  pp. 573-600, 1992. Part 2 of Special Issue on
  Semantic Networks in Artificial Intelligence,
  Fritz Lehmann, editor. Also reprinted on pages
  573-600 of the book, Semantic Networks in
  Artificial Intelligence, Fritz Lehmann, editor,
  Pergammon Press, 1992.

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THE CG MARS LANDER

• References
• 6 R. Levinson and G. Ellis, Multilevel
  hierarchical retrieval,'' Knowledge-Based
  Systems, vol. 5, pp. 233-244, September 1992.
  Special Issue on Conceptual Graphs.
• 7 R. Levinson and G. Fuchs, A pattern-weight
  formulation of search knowledge,'' Tech. Rep.
  UCSC-CRL-91-15, University of California Santa
  Cruz, 2001. Revision to appear in Computational
  Intelligence.
• 8 R. A. Levinson, UDS A universal data
  structure,'' in Proc. 2nd International
  Conference on Conceptual Structures, (College
  Park, Maryland USA), pp. 230-250, 1991.