MCS Thesis

1. MCS Thesis Match-Making in Bartering Scenarios By: Sébastien Mathieu Supervisors: Dr. Virendra C. Bhavsar and Dr. Harold BoleyExamining Board:Dr. John DeDourek, Dr. Weichang Du, Dr. Donglei Du December 5th, 2005

2. Agenda • Introduction • Background • Bartering Trees • Tree Approximation • Ring Bartering Algorithm • Computational Results • Conclusion

3. Introduction (1/5) • Internet as a market place • Web portals • Simple portals ( www.amazon.com ) • Match-making portals ( www.telezoo.com ) • Bartering portals ( www.tandcglobal.com ) • Advanced portal proposals ( www.teclantic.ca )

4. Introduction (2/5) • BarteringThe practice of exchanging goods or services without using the medium of money [2]

5. Introduction (3/5) • Bartering Agent2 Agent1 Similarity1 Aggregate Similarity Similarity2 Offer2 Seek1 Seek2 Offer1

6. Introduction (4/5) • Ring Bartering Agent1 Agent2 Similarity1 Offer2 Seek1 Offer1 Seek2 Agent3 Seek3 Similarity4 >> Similarity2 Similarity3 >> Similarity2 Offer3

7. Introduction (5/5) • Ring Bartering Agent2 s2 O S Agent1 O S s1 … sn sk-1 Agentn O S Agentk O S sn-1 sk sn-2 … Agentn-1 O S

8. Background (1/4) • Different match-making techniques • IBM Websphere  rules and properties • Agent-Mediated eCommerce System with Decision Analysis Features [15] • Bhavsar/Boley/Yang Tree similarity algorithm [1,11,12,15,16]

9. Background (2/4) • Arc labelled weighted trees • Labels on Nodes, fanout-unique labels on Arcs • Relative importance on Arcs  weights ( Σwi = 1.0)

10. Background (3/4) • Similarity Algorithm • Computes the similarity between two arc labeled weighted trees • Top-down traversal / Bottom-up computation • Can handle trees having different arc labels and structures

11. Background (4/4) • Different bartering approaches • The Trade Balance Problem [12] • Multi-Agent Learning Improvement [20] • Ring Bartering in P2P [3]

12. Bartering Trees (1/3)

13. Bartering Trees (2/3) • Computing the Aggregate Similarity • Arithmetic mean not judicious E.g.: Similarity ( Offer1, Seek2 ) = 1.0 Similarity ( Seek1, Offer2 ) = 0.0 Aggregate similarity = 0.5 ?

14. Bartering Trees (2/3) • Computing the Aggregate Similarity • Arithmetic mean not judicious E.g.: Similarity ( Offer1, Seek2 ) = 1.0 Similarity ( Seek1, Offer2 ) = 0.0 Aggregate similarity = 0.5 ? Aggregate similarity ~ 0.3 = (Aggregate similarity reasonably less than 0.5)

15. Bartering Trees (3/3) The Aggregation Function with a = -1.5

16. Motivations To represent our Trees in a multi-dimensional space and use spatial data-structures To avoid the computation of all similarity values Concepts Base: Set of Trees formed by all possible unary treesThe maximum depth is the level of the base The lower the level, the greater the approximation Dimension: Number of Trees in the base Tree Approximation (1/3)

17. Tree Approximation (1/3)

18. Tree Approximation (2/3) • Notion of Distance

19. Tree Approximation (3/3) • Behavior of Distance against Similarity

20. Notion of Risk • The risk takes into account: • The number of participants in the trade • The similarities between the corresponding seeks and offers that are involved in the trade

21. Ring Bartering Algorithm (1/6) • Our algorithm • Returns the (finite) set of rings starting from a given agent • Divided into three main phases: • Repeated selection of the closest Offers (for a given Seek)  first pruning step • Closure of the ring • Testing of the risk  second pruning step

22. Ring Bartering Algorithm (2/6) • Overall Algorithm

23. Ring Bartering Algorithm (3/6) • Selection of the closest Offers

24. Ring Bartering Algorithm (4/6) • Closure of the ring

25. Ring Bartering Algorithm (5/6) • Testing of the risk • Ideal Agent = Agent having similarity equal to one with both the previous and the following agent in the ring

26. Ring Bartering Algorithm (6/6) • Properties of our algorithm • A ring starting from an Agentj of the agent database will be reported by the algorithm, called with Agentj as argument, if and only if it is Dmax/Rmax acceptable • Suppose a ring is reported by the algorithm when starting with a given agent. This ring, will be also reported if we start the algorithm with any of the other agents in the ring Dmax= Maximum DistanceRmax = Maximum RiskDmax/Rmaxacceptable = Risk belowRmax,all Distances belowDmax

27. Computational Results (1/4) • Influence of the Distance • Highest Missing Ring = Similarity of the first missing ring when sorted by aggregate similarity • Number of Highest non Missing Rings = Number of Rings before the first missing ring when sorted by aggregate similarity

28. Computational Results (2/4) • Influence of the Risk

29. Computational Results (3/4) • Computation Time and Size of the Rings

30. Computational Results (4/4) • Computation Time without Pruning (ie Dmax= ∞ and Rmax = 1)

31. We moved from the restrictive buyer/seller scenario to bartering and ring bartering scenarios We developed an efficient algorithm using two pruning techniques based on the notions of Distance and Risk Conclusion (1/2)

32. Future Work Pairing: to create the best combination of rings involving every agent in the virtual market place exactly once Local Similarity: can improve our tree approximation by adding information without increasing the number of dimensions Transfer tree approximation technique back to indexing in non-bartering scenario Conclusion (2/2)

33. Questions ? Thanks !

34. A zero Distance example with a low similarity for a level 1 base

35. Seller weights: an example Seller1 emphasizes his/her pool  easier negotiation phase

36. An example of Base  Bases of dimension 5 and 2