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