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Using additional Using additional information in DisCSPs information in DisCSPs
searchsearch
Prof. Amnon Meisels and Mr. Prof. Amnon Meisels and Mr. Oz Lavee Oz Lavee
Ben Gurion UniversityBen Gurion University
IsraelIsrael
Over ViewOver View
Privacy in the DisCSP –earlier work.Privacy in the DisCSP –earlier work. The meeting scheduling problem.The meeting scheduling problem. The ABT-CBJ , multi variable ABT The ABT-CBJ , multi variable ABT
algorithm.algorithm. Privacy in asynchronous search.Privacy in asynchronous search. Volunteering information in ABT Volunteering information in ABT
algorithm.algorithm. Experimental resultExperimental result
Privacy in DisCSPPrivacy in DisCSP One of the reasons for using distributed One of the reasons for using distributed
search is privacy.search is privacy.
Earlier Work:Earlier Work: Secure Distributed Constraint Satisfaction:Secure Distributed Constraint Satisfaction:
- M. Yokoo et. al.- M. Yokoo et. al. Distributed Forward checking Distributed Forward checking
– – I. Brito and P. Meseguer.I. Brito and P. Meseguer. Privacy/efficiency tradeoff and information Privacy/efficiency tradeoff and information
reasoning reasoning – – Wallace et. al.Wallace et. al.
The goal The goal
This work is inspired from the work of Wallace et. al.This work is inspired from the work of Wallace et. al.
In this work, we tried to understand In this work, we tried to understand the relation between the level of the relation between the level of information revealing and the information revealing and the efficiency of the DisCSP search efficiency of the DisCSP search process.process.
Meeting Scheduling ProblemMeeting Scheduling Problem(MSP)(MSP)
Coordinating meetings among agents Coordinating meetings among agents where all agents can attend their meetings.where all agents can attend their meetings.
Characteristic:Characteristic:• Real world problem.Real world problem.
• Has a distributed structure.Has a distributed structure.
• Information privacy –Information privacy –
agents will not want to reveal information regarding agents will not want to reveal information regarding
their calendar and their meetings their calendar and their meetings
Meeting Scheduling Problem Meeting Scheduling Problem Wallace et. al.Wallace et. al.
Each agent has his own calendar with Each agent has his own calendar with private meetings private meetings
Each meeting consist of <Time,Place> and Each meeting consist of <Time,Place> and it is one hour long.it is one hour long.
Goal:Goal:
- - Schedule a meeting that all Agents can Schedule a meeting that all Agents can attend with respect to the traveling time attend with respect to the traveling time from their own private meetings.from their own private meetings.
Meeting scheduling problemMeeting scheduling problem
Drawbacks at wallace MSPDrawbacks at wallace MSP• One meeting to be scheduled , can be solved in One meeting to be scheduled , can be solved in
polynomial time.polynomial time.
• Synchronous search process.Synchronous search process.
In order to extend the Meeting Scheduling In order to extend the Meeting Scheduling
Problem to a more realistic search problem :Problem to a more realistic search problem :• Several meetings to be scheduled.Several meetings to be scheduled.• In each meeting there is a different sub group In each meeting there is a different sub group
of participants.of participants.
Meeting Scheduling problemMeeting Scheduling problem Group Group S S of of mm agents agents Group Group TT of of nn meetings meetings Each meeting is associated with a set Each meeting is associated with a set ssi i S S of of
agents that attend it.agents that attend it. Each meeting is associated with a location Each meeting is associated with a location
Goal:Goal: Schedule time for every meeting that enable all Schedule time for every meeting that enable all
the participants to travel among their meetingsthe participants to travel among their meetings
Remark – no private meetings.Remark – no private meetings.
Meeting Scheduling as Centralized Meeting Scheduling as Centralized CSPCSP
AA11 attends m attends m11 ,m ,m33 ,m ,m44
AA22 attends m attends m22 ,m ,m44
AA33 attends m attends m11 ,m ,m22
AA44 attends m attends m22 ,m ,m33
AC- Arriving ConstraintAC- Arriving Constraint
m1
m3m4
m2
AC
AC
ACAC
AC
AC
Meeting Scheduling as DisCSPMeeting Scheduling as DisCSP
x11
x22
x13 x2
3
x42
x44
x32
x31
x14
A1 A2
A3 A4
=
=
==
=
=
ACAC
ACAC
AC
AC
ABT-CBJ AlgorithmABT-CBJ Algorithm
For this multi variable per agent problem, we used For this multi variable per agent problem, we used
the ABT-CBJ algorithm:the ABT-CBJ algorithm:
Multi Variable per agent. Multi Variable per agent.
ABT Based algorithm.ABT Based algorithm.
In each step, agent’s variables are assigned In each step, agent’s variables are assigned
according to the CBJ algorithm.according to the CBJ algorithm.
Assumption: agent variables are in a successive Assumption: agent variables are in a successive order among the total order of variables. order among the total order of variables.
Privacy measurementPrivacy measurement
What is information in an asynchronous What is information in an asynchronous distributed search process?distributed search process?
What is an information unit ?What is an information unit ?
What is the value of an information unit?What is the value of an information unit?
OK? MessageOK? Message
The agent state and the Assigned values The agent state and the Assigned values are change asynchronously. are change asynchronously.
The validity of the information retrieved The validity of the information retrieved from an OK? Message on the sending from an OK? Message on the sending agent state is temporal. agent state is temporal.
Xi
<Ok?, Xi= 12>
<Ok?, Xi= 5>
<Ok?, Xi= 2>
Nogood messageNogood message A nogood is always correct.A nogood is always correct.
Nogood can be referred as an information Nogood can be referred as an information unit. unit.
The value of a nogood is the ratio of the The value of a nogood is the ratio of the eliminated subtree with the total search eliminated subtree with the total search space space
Value(ng<xValue(ng<x11=v=v11,…,x,…,xii=v=vii>) =>) =
DDi+1i+1*…*D*…*Dn n /D/D11*…*D*…*Dnn
Nogood as information unit Nogood as information unit
Reducing the number of nogood sent Reducing the number of nogood sent in the search process may affect the in the search process may affect the completeness of the search.completeness of the search.
on the other hand:on the other hand:
Does Volunteering additional Does Volunteering additional
nogoods will improve the search nogoods will improve the search
process?process?
Additional nogoods in MSPAdditional nogoods in MSP
Generating additional nogoods in Generating additional nogoods in MSP does not require many CC’s.MSP does not require many CC’s.
A2 A5
A8
x23
x84
x83
x54
AC
<x23= Rome,Mon,14:00> <x5
4= Paris,Mon,14:00>
Additional nogoods in MSPAdditional nogoods in MSP
Generating additional nogoods in Generating additional nogoods in MSP does not require many CC’s.MSP does not require many CC’s.
A2 A5
A8
x23
x84
x83
x54
AC
<x23= Rome,Mon,14:00> <x5
4= Paris,Mon,14:00>
Conflict
Additional nogoods in MSPAdditional nogoods in MSP
Generating additional nogoods in Generating additional nogoods in MSP does not require many CC’s.MSP does not require many CC’s.
A2 A5
A8
x23
x84
x83
x54
AC
NoGood(x23= Rome,Mon,14:00 ,x5
4=Paris,Mon,14:00>)
Conflict
Additional nogoods in MSPAdditional nogoods in MSP
Generating additional nogoods in Generating additional nogoods in MSP does not require many CC’s.MSP does not require many CC’s.
A2 A5
A8
x23
x84
x83
x54
AC
NoGood(x23= Rome,Mon,14:00 , x5
4 =Paris,Mon,14:00>)
Conflict
NoGood(x23= Rome,Mon,14:00 , x5
4 =Paris,Mon,15:00>)
The Experiment The Experiment
16 - agents16 - agents 9 - meetings9 - meetings 3 - meeting per agent3 - meeting per agent 24 - domain size24 - domain size 2 different distance matrixes 2 different distance matrixes
Experimental ResultExperimental Result
CCC's
0
100000
200000
300000
400000
500000
600000
700000
0 1 2 4 6 8 9
Messages
0
5000
10000
15000
20000
25000
30000
0 1 2 4 6 8 9
Messages and CCC’s Vs. number of additional nogood in a message
Privacy MeasurementsPrivacy Measurements
steps vs. information sent
0
20
40
60
80
100
120
0 0.1 0.2 0.3 0.4 0.5
Steps
CCC's vs. information sent
0
1000
2000
3000
4000
5000
6000
0 0.1 0.2 0.3 0.4 0.5
cccs
Performance measurements Vs. information sent ratio
ConclusionConclusion
The Meeting scheduling problem as a The Meeting scheduling problem as a DisCSP DisCSP
aspect of information in an aspect of information in an asynchronous search.asynchronous search.
The influence of volunteering The influence of volunteering information on the efficiency of the information on the efficiency of the search processsearch process