Transcript 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.

A Weighted-Tree Similarity Algorithm for
Multi-Agent Systems in e-Business
Environments
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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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Introduction
Multi-agent system architecture
Tree representation
Similarity of trees
Experimental results
Conclusion
Introduction
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
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e-business, e-learning.
Semantic Web and Web Services.
–
Virtual marketplace.
–
Buyer-seller message exchange.
Semantic match-making in multiagent systems.
–
3
Keywords/keyphrases.
Multi-agent system architecture
Main
User Info
Agents
…
User Profiles
User Agents
…
…
User
Web
Browser
Server
To other sites
(network)
…CafeCafe-1 n Cafe-n
4
Agent-based Community Oriented Routing Network (ACORN)
Tree representation

Why tree representation?
–
–
Flexibly represent complex structures.
Why arc-labelled, arc-weighted tree?
Car
Car
Make
Year
0.5
0.3
Model
0.2
Ford
5
Explorer
2002
Ford
Explorer
2002
Matchmaking of agents

Match-making in the Cafe.
Leaner 1
Course 1
Leaner 2
.
.
.
Course 2
.
.
.
Cafe
Course m
Leaner n
Programming
in Java
Programming
in Java
Tuition
Credit Duration
0.4
0.2
0.1 Textbook
0.3
3
6
2 months Thinking $1200
in Java
Tuition
Credit Duration
0.4
0.2
0.1 Textbook
0.3
3
2 months Introduction $1500
to Java
Tree representation - lexicographic order

The arcs are labelled in lexicographic
(alphabetical) order.
Hotel
Car
Make
0.5
0.5
Beds
0.5
Model
Queen
0.2
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Location
Year
0.3
Ford
Capacity
Explorer
0.8
2002
A tree describing “Car”.
100
Fredericton
Downtown
Single
0.9
0.2
150 Lincoln
Hotel
A tree describing “Hotel”.
Uptown
0.1
Sheraton
Hotel
Tree representation - depth and breadth

The depth and breadth of any subtree are not
limited.
Jobbank
Newpost
0.9
Oldpost
0.1
IT
Hardware
0.2
…
Java
0.5
Education
Software
0.8
Advanced
0.4
Preliminary
School
Position
…
Oracle
College High
0.4
University
Certificate
0.1
School
0.5
0.5
Programmer
8
0.6
DBA Seneca Liverpool UNB
College High School
A tree that describes “Jobbank”.
Serialization of trees
–
Weighted Object-Oriented RuleML.
–
XML attributes for arc labels and weights.
cterm[ -opc[ctor[car]],
<cterm>
-r[n[make],w[0.3]][ind[ford]],
<_opc><ctor>Car</ctor></_opc>
-r[n[model],w[0.2]][ind[explorer],
<_r n=“Make” w=“0.3”><ind>Ford</ind></_r>
-r[n[year],w[0.5]][ind[1999]]
<_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.
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Tree representation in Relfun.
Similarity of trees – simple trees
tree t
Make
0.3
Ford
10
tree t´
Car
1
Year
0.7
2002
Car (House)
Year
0.7
Make
0.3
1999
Ford
0
Similarity of trees – complex trees
tree t´
vehicle
tree t
summer
autumn
0.5
0.5
auto
auto
make
year
make
year
0.3334
0.3333
0.3334
model 0.3333
model
ford
big
0.5
e-series
wagon
11
ford
1999
mini
big
0.5
0.3333
free
star
van
2000
mini
0.5
0.5
montery free
star
 si(wi + w'i)/2

0.5
auto
auto
make
year
make
year 0.3334
0.3333
0.3334 model 0.3333
model
0.3333
van
summer
autumn
0.5
0.3333
vehicle
ford
big
0.5
e-series
wagon
0.3333
van
1999
mini
ford truck
2001
0.5
free
star
 A(si)(wi + w'i)/2
A(si) = si
A(si) = si .
Algorithm for tree similarity
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Three main recursive functions of the algorithm.
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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.
Experimental results –simple trees
Experiments
Tree
make
1
auto
year
0.5
0.5
ford
t1
auto
1.0
0.0
ford
2
2002
t1
auto
year
make
0.0
ford
13
2002
year
make
1.0
t3
Results
Tree
2002
make
auto
year
0.5
0.5
0.1
chrysler t2
1998
auto
make
year
1.0
ford
make
0.0
t2
auto
1.0
ford
1998
year
0.0
t4
0.5
2002
1.0
Experimental results – simple trees
(cont’d)
Experiments
Tree
Tree
auto
auto
model
1.0
3
mustang
ford explorer 2000
t1
t2
auto
auto
model
1.0
14
year
make
0.45 model 0.45
0.1
year
make
model 0.05
0.05
0.9
mustang
ford explorer 2000
t3
t4
Results
0.2823
0.1203
Experimental results – identical tree
structures
Experiments
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Tree
Tree
auto
auto
yea
make
0.3 model r 0.5
0.2
make model year
0.3
0.2 0.5
ford explorer 2002
ford explorer 1999
t1
t2
auto
auto
make
year
make model yea
model
0.3334 0.3333 r0.3333 0.3334 0.3333 0.3333
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ford explorer 2002
ford explorer 1999
t3
t4
Results
0.55
0.7000
Experimental results – progressively
complex trees
Experiments
Tree
Tree
Results
auto
t2
make
1.0
auto
5
ford
auto
t3
model
0.5
make
0.5
t1
ford
t4
0.3025
explorer
auto
year
make
model
0.5
0.3
0.2
ford explorer 2002
16
0.3025
0.3025
Experimental results – complex trees
Tree
Experiments
vehicle
autumn
0.5
0.3333
ford van
1999
2000
mini big
mini
e-series free
wagon star
0.5
0.5
auto
auto
make
make
year 0.3334 year
0.3334
0.3333
model 0.3333 model
0.5
e-series free
wagon star
tree t1
ford
big
0.5
e-series
wagon
0.5950
0.3333
0.3333
van
0.5
summer
0.5
auto
auto
make
year
year
make
0.3334
0.3333
0.3334 model
model 0.3333
ford
big
17
autumn
0.5
0.3333
si
vehicle
summer
0.5
6
Si
Tree
ford
van
1999 van 2001
mini
0.5
free
star
tree t2
0.7611
Experimental results – complex trees
(cont’d)
Experiments
Tree
vehicle
autumn
summer
0.5
0.5
1.0
auto
make
year
0.3334 model 0.3333
auto
0.3334
ford van
make
0.3334
0.3333
model
2000
year
0.3333
0.3333
0.3333
ford
tree t1
model
0.5894
auto
year
make
0.3333
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si
vehicle
summer
7
Si
Tree
van 1994 ford van
tree t2
0.6816
2001
Conclusion
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Tree representations – useful for e-Business, eLearning.
Matchmaking in multiagent systems – a versatile
tree similarity algorithm is proposed.
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Executable specification available in functional-logic
language: Relfun.
- A Java implementation is in progress.
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Future work - Clustering of agents.
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