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Graph Databases: Efficient storage  and Rapid retrieval 

Graph Databases: Efficient storage  and Rapid retrieval . Robert Levinson Machine Intelligence Laboratory University of California Santa Cruz. THE CG MARS LANDER. English-CG-English Translation. High level architecture. English Discourse. English Queries.

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Graph Databases: Efficient storage  and Rapid retrieval 

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  1. Graph Databases: Efficient storage  and Rapid retrieval  Robert Levinson Machine Intelligence Laboratory University of California Santa Cruz

  2. THE CG MARS LANDER English-CG-English Translation High level architecture 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(n^2) 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.” AB+AC = A(B+C). 

  6. Symmetry Synonyms • similarity • commonality • structure • mutual information • relationship • redundancy

  7. 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 

  10. THE CG MARS LANDER Exploit Tuple-Based Linear CGs !  (a conceptual graph syntax that supports rapid retirieval and question-answering).

  11. @CG000: { AGNT (government, BE) }. • @CG001: { AGNT (Hungarian_American_Enterprise_Fund, invest), OBJ (invest, Dollars | 1000000 ), IN (Dollars | 1000000, first_business) }. • @CG002 : { AGNT (@CG000, manage), OBJ (manage, @CG001) }.

  12. THE CG MARS LANDER A query: /* Q2: Does anybody own the rag newspaper New York Post ? */ Query::@bob_202 : { ISA ( New_York_Post , newspaper [ n34861 ] ) , CHRC ( newspaper [ n34861 ] , rag [ n9 ] ) , AGNT ( own [ v9125 ] , ????? ) , }.

  13. THE CG MARS LANDER Answer:   /* A2: Rupert Murdoch once owned the troubled tabloid newspaper New York Post. */ @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 ) }.

  14. 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. 

  16. 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. N Q Method I Cost Method III Cost 10 10 10 100 100 100 1,000 1,000 1,000 1,000 10,000 10,000 1 10 100 1 10 100 1 10 100 1,000 1,000 10,000 10 100 1,000 100 1,000 10,000 1,000 10,000 100,000 1,000,000 10,000,000 100,000,000 5.0 14.9 104.8 296.6 328.6 688.6 7,293.4 7,374.4 8,184.4 16,284.4 152,823.8 296,823.8 Cost/ benefit table

  18. 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.

  19. 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.

  20. 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.

  21. 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. 

  22. 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.

  23. More references… • [4]R. 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.

  24. 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.

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