1. 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. 2 Outline Introduction Multi-agent system architecture Tree representation Similarity of trees Experimental results Conclusion

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

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

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

6. 6 Matchmaking of agents Match-making in the Cafe..... Cafe Leaner 1.. Course 1 Leaner 2 Leaner n Course 2 Course m Programming in Java Credit Thinking in Java Textbook Tuition Duration $12002 months 3 0.2 0.1 0.3 0.4 carried by Programming in Java Credit Introduction to Java Textbook Tuition Duration $1500 2 months 3 0.2 0.1 0.3 0.4

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

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

9. 9 Serialization of trees – XML attributes for arc labels and weights. – Weighted Object-Oriented RuleML. 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]] ] Car Ford Explorer 1999 Tree serialization in OO RuleML.Tree representation in Relfun.

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

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

12. 12 Algorithm for tree similarity – Treesim(t,t'): Recursively compares any (unordered) pair of trees. Three main recursive functions of the algorithm. – 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. 13 Experimental results –simple trees

14. 14 Experimental results – simple trees (cont’d) Experiments Tree Results 3 0.1 make auto mustang auto 0.45 model 2000 ford year t1t1 t2t2 1.0 model 0.45 explorer 0.9 make auto mustang auto 0.05 model 2000 ford year t3t3 t4t4 1.0 model 0.05 explorer 0.2823 0.1203

15. 15 Experimental results – identical tree structures ExperimentsTree Results 4 0.2 make auto 0.3 1999 ford year t2t2 model 0.5 explorer make auto 1999 ford year t4t4 model explorer 0.3333 0.3334 0.2 make auto 0.3 2002 ford yea r t1t1 model 0.5 explorer make 2002 ford yea r t3t3 model explorer 0.3333 0.3334 auto 0.55 0.7000

16. 16 Experimental results – progressively complex trees ExperimentsTree Results 5 auto t1t1 t2t2 make 1.0 ford auto model fordexplorer make 0.5 t3t3 auto model year ford explorer 2002 make 0.3 0.2 0.5 t4t4 0.3025

17. 17 Experimental results – complex trees vehicle autumn auto make 0.5 model year 0.3334 ford mini 1999 summer make model year 0.3334 0.3333 ford 2000 free star free star e-series wagon e-series wagon 0.5 vehicle autumn auto make 0.5 model year 0.3334 ford van 1999 summer make model year 0.3334 0.3333 ford 2001 free star e-series wagon 0.5 tree t 1 tree t 2 big mini SiSi Experiments Tree 6 0.5950 0.7611 big van

18. 18 Experimental results – complex trees (cont’d) SiSi Experiments Tree 7 vehicle auto 1.0 0.3334 summer make model year 0.3333 ford 2000 tree t 1 vehicle autumn auto make 0.5 model year 0.3334 ford 1994 summer make model year 0.3334 0.3333 ford 2001 tree t 2 0.5894 0.6816 van

19. 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. Future work - Clustering of agents. - A Java implementation is in progress.

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