Using additional information in DisCSPs search

1
Using additional information in DisCSPs search

• Prof. Amnon Meisels and Mr. Oz Lavee
• Ben Gurion University
• Israel

2
Over View

• Privacy in the DisCSP earlier work.
• The meeting scheduling problem.
• The ABT-CBJ , multi variable ABT algorithm.
• Privacy in asynchronous search.
• Volunteering information in ABT algorithm.
• Experimental result

3
Privacy in DisCSP

• One of the reasons for using distributed search
  is privacy.
• Earlier Work
• Secure Distributed Constraint Satisfaction
• - M. Yokoo et. al.
• Distributed Forward checking
• I. Brito and P. Meseguer.
• Privacy/efficiency tradeoff and information
  reasoning
• Wallace et. al.

4
The goal

• This work is inspired from the work of Wallace
  et. al.
• In this work, we tried to understand the relation
  between the level of information revealing and
  the efficiency of the DisCSP search process.

5
Meeting Scheduling Problem(MSP)

• Coordinating meetings among agents
• where all agents can attend their meetings.
• Characteristic
• Real world problem.
• Has a distributed structure.
• Information privacy
• agents will not want to reveal information
  regarding their calendar and their meetings

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Meeting Scheduling Problem Wallace et. al.

• Each agent has his own calendar with private
  meetings
• Each meeting consist of ltTime,Placegt and it is
  one hour long.
• Goal
• - Schedule a meeting that all Agents can attend
  with respect to the traveling time from their own
  private meetings.

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Meeting scheduling problem

• Drawbacks at wallace MSP
• One meeting to be scheduled , can be solved in
  polynomial time.
• Synchronous search process.
• In order to extend the Meeting Scheduling
  Problem to a more realistic search problem
• Several meetings to be scheduled.
• In each meeting there is a different sub group of
  participants.

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Meeting Scheduling problem

• Group S of m agents
• Group T of n meetings
• Each meeting is associated with a set si ? S of
  agents that attend it.
• Each meeting is associated with a location
• Goal
• Schedule time for every meeting that enable all
  the participants to travel among their meetings
• Remark no private meetings.

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Meeting Scheduling as Centralized CSP

• A1 attends m1 ,m3 ,m4
• A2 attends m2 ,m4
• A3 attends m1 ,m2
• A4 attends m2 ,m3
• AC- Arriving Constraint

m1
m2
AC
AC
AC
AC
AC
m3
m4
AC
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Meeting Scheduling as DisCSP
A1
A2
x11
x13
x23

AC
x22
AC
AC
AC
x14




A3
A4
x44
x31
AC
AC
x42
x32
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ABT-CBJ Algorithm

• For this multi variable per agent problem, we
  used the ABT-CBJ algorithm
• Multi Variable per agent.
• ABT Based algorithm.
• In each step, agents variables are assigned
  according to the CBJ algorithm.
• Assumption agent variables are in a successive
  order among the total order of variables.

12
Privacy measurement

• What is information in an asynchronous
  distributed search process?
• What is an information unit ?
• What is the value of an information unit?

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OK? Message

• The agent state and the Assigned values are
  change asynchronously.
• The validity of the information retrieved from an
  OK? Message on the sending agent state is
  temporal.

Xi
ltOk?, Xi 5gt
ltOk?, Xi 12gt
ltOk?, Xi 2gt
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Nogood message

• A nogood is always correct.
• Nogood can be referred as an information unit.
• The value of a nogood is the ratio of the
  eliminated subtree with the total search space
• Value(ngltx1v1,,xivigt)
• Di1Dn /D1Dn

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Nogood as information unit

• Reducing the number of nogood sent in the search
  process may affect the completeness of the
  search.
• on the other hand
• Does Volunteering additional nogoods will improve
  the search process?

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Additional nogoods in MSP

• Generating additional nogoods in MSP does not
  require many CCs.

A2
A5
x23
x54
ltx23 Rome,Mon,1400gt
ltx54 Paris,Mon,1400gt
x83
x84
AC
A8
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Additional nogoods in MSP

• Generating additional nogoods in MSP does not
  require many CCs.

A2
A5
x23
x54
ltx23 Rome,Mon,1400gt
ltx54 Paris,Mon,1400gt
Conflict
x83
x84
AC
A8
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Additional nogoods in MSP

• Generating additional nogoods in MSP does not
  require many CCs.

A2
A5
x23
x54
NoGood(x23 Rome,Mon,1400 ,x54Paris,Mon,1400gt)
Conflict
x83
x84
AC
A8
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Additional nogoods in MSP

• Generating additional nogoods in MSP does not
  require many CCs.

A2
A5
x23
x54
NoGood(x23 Rome,Mon,1400 , x54
Paris,Mon,1400gt)
NoGood(x23 Rome,Mon,1400 , x54
Paris,Mon,1500gt)
Conflict
x83
x84
AC
A8
20
The Experiment

• 16 - agents
• 9 - meetings
• 3 - meeting per agent
• 24 - domain size
• 2 different distance matrixes

21
Experimental Result
Messages and CCCs Vs. number of additional
nogood in a message
22
Privacy Measurements
Performance measurements Vs. information sent
ratio
23
Conclusion

• The Meeting scheduling problem as a DisCSP
• aspect of information in an asynchronous search.
• The influence of volunteering information on the
  efficiency of the search process

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The End