MCS ThesisMCS Thesis

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

Match-Making

in Bartering Scenarios

22

AgendaAgenda

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

33

Introduction (1/5)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 )

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Introduction (2/5)Introduction (2/5)

• Bartering

The practice of exchanging goods or services without using the medium of money [2]

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Introduction (3/5)Introduction (3/5)

• Bartering

Seek2Offer1

Seek1 Offer2

Agent1 Agent2Similarity1

Aggregate

Similarity

Similarity2

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Introduction (4/5)Introduction (4/5)

• Ring Bartering

Seek2Offer1

Seek1 Offer2

Agent1 Agent2

Similarity1

Offer3

Seek3

Agent3

Similarity4 >> Similarity2

Similarity3 >> Similarity2

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Introduction (5/5)Introduction (5/5)

• Ring Bartering

Agent1O S Agent2O S

AgentkO S

Agentn-1O S

AgentnO S

…

…

s1

s2

sk-1

sk

sn-2

sn-1

sn

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Background (1/4)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]

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Background (2/4)Background (2/4)

• Arc labelled weighted trees

• Labels on Nodes, fanout-unique labels on Arcs

• Relative importance on Arcs weights ( Σwi = 1.0)

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Background (3/4)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

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Background (4/4)Background (4/4)

• Different bartering approaches

– The Trade Balance Problem [12]

– Multi-Agent Learning Improvement [20]

– Ring Bartering in P2P [3]

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Bartering Trees (1/3)Bartering Trees (1/3)

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Bartering Trees (2/3)Bartering Trees (2/3)

• Computing the Aggregate SimilarityArithmetic mean not judicious

E.g.: Similarity ( Offer1, Seek2 ) = 1.0 Similarity ( Seek1, Offer2 ) = 0.0

Aggregate similarity = 0.5?

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Bartering Trees (2/3)Bartering Trees (2/3)

• Computing the Aggregate SimilarityArithmetic 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)

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Bartering Trees (3/3)Bartering Trees (3/3)

The Aggregation Function with a = -1.5

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Tree Approximation (1/3) 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

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Tree Approximation (1/3) Tree Approximation (1/3)

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Tree Approximation (2/3)Tree Approximation (2/3)

• Notion of Distance

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Tree Approximation (3/3)Tree Approximation (3/3)

• Behavior of Distance against Similarity

2020

Notion of RiskNotion 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

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Ring Bartering Algorithm (1/6)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

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Ring Bartering Algorithm (2/6)Ring Bartering Algorithm (2/6)

• Overall Algorithm

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Ring Bartering Algorithm (3/6)Ring Bartering Algorithm (3/6)

• Selection of the closest Offers

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Ring Bartering Algorithm (4/6)Ring Bartering Algorithm (4/6)

• Closure of the ring

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Ring Bartering Algorithm (5/6)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

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Ring Bartering Algorithm (6/6)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 below Rmax, all Distances below Dmax

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Computational Results (1/4)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

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Computational Results (2/4)Computational Results (2/4)

• Influence of the Risk

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Computational Results (3/4)Computational Results (3/4)

• Computation Time and Size of the Rings

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Computational Results (4/4)Computational Results (4/4)

• Computation Time without Pruning (ie Dmax = ∞ and Rmax = 1)

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Conclusion (1/2)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

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Conclusion (2/2)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

3333

Questions ?Questions ?

Thanks !

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

3535

• Seller weights: an example

Seller1 emphasizes his/her pool easier negotiation phase

3636

• An example of Base

Bases of dimension 5 and 2