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A Weighted-Tree Similarity Algorithm for Multi-A gent Systems in e-Business Environments

A Weighted-Tree Similarity Algorithm for Multi-A gent Systems in e-Business Environments. Virendra C.Bhavsar* Harold Boley** Lu Yang* * Faculty of Computer Science, Univ. of New Brunswick, Fredericton ** Institute for Information Technology – e-Business, NRC, Fredericton. Outline.

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A Weighted-Tree Similarity Algorithm for Multi-A gent Systems in e-Business Environments

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  1. A Weighted-Tree Similarity Algorithm for Multi-Agent Systems in e-Business Environments Virendra C.Bhavsar* Harold Boley** Lu Yang* *Faculty of Computer Science, Univ. of New Brunswick, Fredericton **Institute for Information Technology – e-Business, NRC, Fredericton

  2. Outline • Introduction • Multi-agent system architecture • Tree representation • Similarity of trees • Experimental results • Conclusion

  3. Introduction • e-business, e-learning. • Semantic Web and Web Services. • Virtual marketplace. • Buyer-seller message exchange. • Semantic match-making in multiagent systems. • Keywords/keyphrases.

  4. Main Server Agents User Info Web Browser User Profiles … User … User Agents … To other sites (network) … Cafe-n Cafe-n Cafe-1 Multi-agent system architecture Agent-based Community Oriented Routing Network (ACORN)

  5. 0.5 0.3 0.2 Car Car Make Year Model 2002 Explorer Ford 2002 Explorer Ford Tree representation • Why tree representation? • Flexibly represent complex structures. • Why arc-labelled, arc-weighted tree?

  6. Leaner 1 Course 1 carried by Leaner 2 Course 2 carried by . . Cafe . . . . Course m Leaner n Programming inJava Programming inJava Tuition Credit Tuition 0.4 Duration Credit 0.2 0.4 Textbook Duration 0.1 0.2 0.3 Textbook 0.1 0.3 2 months Thinking in Java $1200 3 $1500 2 months Introduction to Java 3 Matchmaking of agents • Match-making in the Cafe.

  7. Car Make Year 0.5 0.3 Model 0.2 Ford 2002 Explorer Tree representation - lexicographic order • The arcs are labelled in lexicographic (alphabetical) order. Hotel Location Capacity 0.5 0.5 Beds Fredericton Downtown Queen 0.9 Uptown Single 0.8 0.1 0.2 Lincoln Hotel Sheraton Hotel 100 150 A tree describing “Car”. A tree describing “Hotel”.

  8. Tree representation - depth and breadth • The depth and breadth of any subtree are not limited. Jobbank Oldpost Newpost 0.9 0.1 IT Education Advanced Software Preliminary Hardware 0.4 0.8 0.6 0.2 School Position … … Oracle Certificate College High School Java University 0.4 0.1 0.5 0.5 0.5 Seneca College Liverpool HighSchool UNB Programmer DBA A tree that describes “Jobbank”.

  9. cterm[ -opc[ctor[car]], -r[n[make],w[0.3]][ind[ford]], -r[n[model],w[0.2]][ind[explorer], -r[n[year],w[0.5]][ind[1999]] ] <cterm> <_opc><ctor>Car</ctor></_opc> <_r n=“Make” w=“0.3”><ind>Ford</ind></_r> <_r n=“Model” w=“0.2”><ind>Explorer</ind></_r> <_r n=“Year” w=“0.5”><ind>1999</ind></_r> </cterm> Tree serialization in OO RuleML. Tree representation in Relfun. Serialization of trees • Weighted Object-Oriented RuleML. • XML attributes forarc labels and weights.

  10. tree t tree t´ Car Car Make Year Year Make 0.7 0.3 0.7 0.3 2002 Ford 1999 Ford 0 1 Similarity of trees – simple trees (House)

  11. A(si) = si A(si) = . Similarity of trees – complex trees tree t´ tree t vehicle vehicle autumn summer autumn summer 0.5 0.5 0.5 0.5 auto auto auto auto make make year year make year make year 0.3334 0.3334 0.3333 0.3333 0.3334 0.3334 model 0.3333 0.3333 model model model 0.3333 0.3333 0.3333 0.3333 van ford van van ford truck ford ford 1999 1999 2000 2001 mini big big big mini mini 0.5 0.5 0.5 0.5 0.5 0.5 free star e-series wagon e-series wagon free star montery free star  si(wi + w'i)/2 A(si)(wi + w'i)/2 

  12. Algorithm for tree similarity • Three main recursive functions of the algorithm. • Treesim(t,t'): Recursively compares any (unordered) pair of trees. • Treemap(l,l'):Co-recursively maps two lists, l and l', of labelled • and weighted arcs: descends into identical–labelled subtrees. • Treeplicity(i,t): Decreases the similarity with decreasing simplicity.

  13. Experiments Results Tree Tree auto auto make make year year 0.1 0.5 0.5 0.5 0.5 1 chrysler ford 2002 t2 1998 t1 auto auto year make make year 0.5 0.0 1.0 1.0 0.0 ford ford 2002 1998 t1 t2 2 auto auto make year year make 1.0 0.0 1.0 0.0 1.0 ford ford 2002 2002 t4 t3 Experimental results –simple trees

  14. Experimental results – simple trees (cont’d) Tree Tree Results Experiments auto auto year make model model 0.45 0.45 0.2823 1.0 0.1 2000 explorer ford mustang t1 t2 3 auto auto year make model model 0.05 0.05 1.0 0.9 0.1203 explorer 2000 ford mustang t3 t4

  15. Experimental results – identical tree structures Results Experiments Tree Tree auto auto year year make make model model 0.3 0.5 0.5 0.3 0.2 0.2 0.55 1999 explorer ford explorer 2002 ford t2 t1 4 auto auto make year year make model model 0.3334 0.3333 0.3334 0.3333 0.3333 0.3333 0.7000 explorer ford explorer ford 2002 1999 t3 t4

  16. Experimental results – progressively complex trees Tree Experiments Tree Results auto t2 make 0.3025 1.0 ford auto auto t3 model make 5 0.5 0.5 0.3025 t1 ford explorer t4 auto year make model 0.5 0.3 0.3025 0.2 2002 explorer ford

  17. Experimental results – complex trees Si Tree Tree Experiments vehicle vehicle autumn summer autumn summer 0.5 0.5 0.5 0.5 0.5950 auto auto auto auto make year make year year make make year 0.3334 0.3333 0.3334 0.3334 0.3333 6 0.3333 model 0.3334 0.3333 model model model 0.3333 0.3333 0.3333 0.3333 ford ford van van van ford ford van 1999 2000 1999 2001 mini big big big mini mini 0.7611 0.5 0.5 0.5 0.5 0.5 0.5 free star e-series wagon free star e-series wagon free star e-series wagon tree t2 tree t1

  18. Experimental results – complex trees (cont’d) Si Experiments Tree Tree vehicle vehicle summer autumn summer 0.5894 0.5 0.5 1.0 auto auto auto 7 make year make year make 0.3334 year 0.3333 model 0.3334 0.3333 0.3334 model model 0.3333 0.3333 0.6816 0.3333 0.3333 2000 van ford 2001 ford van 1994 van ford tree t1 tree t2

  19. Conclusion • Tree representations – useful for e-Business, e- Learning. • Matchmaking in multiagent systems – a versatile tree similarity algorithm is proposed. • Executable specification available in functional-logic language: Relfun. - A Java implementation is in progress. • Future work - Clustering of agents.

  20. Thank you! ?

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