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

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 ( ) –Match-making portals ( ) –Bartering portals ( ) –Advanced portal proposals ( )

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

5 Introduction (3/5) Bartering Seek 2 Offer 1 Seek 1 Offer 2 Agent 1 Agent 2 Similarity 1 Aggregate Similarity Similarity 2

6 Introduction (4/5) Ring Bartering Seek 2 Offer 1 Seek 1 Offer 2 Agent 1 Agent 2 Similarity 1 Offer 3 Seek 3 Agent 3 Similarity 4 >> Similarity 2 Similarity 3 >> Similarity 2

7 Introduction (5/5) Ring Bartering Agent 1 O S Agent 2 O S Agent k O S Agent n-1 O S Agent n O S … … s1s1 s2s2 s k-1 sksk s n-2 s n-1 snsn

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 ( Σw i = 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 ( Offer 1, Seek 2 ) = 1.0 Similarity ( Seek 1, Offer 2 ) = 0.0 Aggregate similarity = 0.5 ?

14 Bartering Trees (2/3) Computing the Aggregate Similarity  Arithmetic mean not judicious E.g.: Similarity ( Offer 1, Seek 2 ) = 1.0 Similarity ( Seek 1, Offer 2 ) = 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 Tree Approximation (1/3) 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 trees The maximum depth is the level of the base The lower the level, the greater the approximation –Dimension: Number of Trees in the base

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 Agent j of the agent database will be reported by the algorithm, called with Agent j as argument, if and only if it is D max /R max 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 D max = Maximum Distance R max = Maximum Risk D max /R max acceptable = Risk below R max, all Distances below D max

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 D max = ∞ and R max = 1)

31 Conclusion (1/2) 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

32 Conclusion (2/2) 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

33 Questions ? Thanks !

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

35 Seller weights: an example Seller 1 emphasizes his/her pool  easier negotiation phase

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