Using additional information in DisCSPs search Prof. Amnon Meisels and Mr. Oz Lavee Prof. Amnon Meisels and Mr. Oz Lavee Ben Gurion University Israel

Over 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 algorithm. The ABT-CBJ, multi variable ABT algorithm. Privacy in asynchronous search. Privacy in asynchronous search. Volunteering information in ABT algorithm. Volunteering information in ABT algorithm. Experimental result Experimental result

Privacy in DisCSP One of the reasons for using distributed search is privacy. One of the reasons for using distributed search is privacy. 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 reasoning Privacy/efficiency tradeoff and information reasoning – Wallace et. al. – Wallace et. al.

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 the relation between the level of information revealing and the efficiency of the DisCSP search process. In this work, we tried to understand the relation between the level of information revealing and the efficiency of the DisCSP search process.

Meeting Scheduling Problem (MSP) Coordinating meetings among agents Coordinating meetings among agents where all agents can attend their meetings. 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 their calendar and their meetings agents will not want to reveal information regarding their calendar and their meetings

Meeting Scheduling Problem Wallace et. al. Each agent has his own calendar with private meetings Each agent has his own calendar with private meetings Each meeting consist of and it is one hour long. Each meeting consist of 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.

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

Meeting Scheduling problem Group S of m agents Group S of m agents Group T of n meetings Group T of n meetings Each meeting is associated with a set s i  S of agents that attend it. Each meeting is associated with a set s i  S of agents that attend it. Each meeting is associated with a location Each meeting is associated with a locationGoal: Schedule time for every meeting that enable all the participants to travel among their meetings Schedule time for every meeting that enable all the participants to travel among their meetings Remark – no private meetings. Remark – no private meetings.

Meeting Scheduling as Centralized CSP A 1 attends m 1,m 3,m 4 A 2 attends m 2,m 4 A 3 attends m 1,m 2 A 4 attends m 2,m 3 AC- Arriving Constraint m1m1 m3m3 m4m4 m2m2 AC

Meeting Scheduling as DisCSP x11x11 x22x22 x13x13 x23x23 x42x42 x44x44 x32x32 x31x31 x14x14 A1A1 A2A2 A3A3 A4A4 = = = = = = AC

ABT-CBJ Algorithm For this multi variable per agent problem, we used 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 according to the CBJ algorithm. In each step, agent’s variables are assigned according to the CBJ algorithm. Assumption: agent variables are in a successive order among the total order of variables.

Privacy measurement What is information in an asynchronous distributed search process? What is information in an asynchronous 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? Message The agent state and the Assigned values are change asynchronously. 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. The validity of the information retrieved from an OK? Message on the sending agent state is temporal. XiXi

Nogood message A nogood is always correct. A nogood is always correct. Nogood can be referred as an information unit. 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 The value of a nogood is the ratio of the eliminated subtree with the total search space Value(ng ) = Value(ng ) = D i+1 *…*D n /D 1 *…*D n

Nogood as information unit Reducing the number of nogood sent in the search process may affect the completeness of the search. 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? Does Volunteering additional nogoods will improve the search process?

Additional nogoods in MSP Generating additional nogoods in MSP does not require many CC’s. Generating additional nogoods in MSP does not require many CC’s. A2A2 A5A5 A8A8 x23x23 x84x84 x83x83 x54x54 AC

Additional nogoods in MSP Generating additional nogoods in MSP does not require many CC’s. Generating additional nogoods in MSP does not require many CC’s. A2A2 A5A5 A8A8 x23x23 x84x84 x83x83 x54x54 AC Conflict

Additional nogoods in MSP Generating additional nogoods in MSP does not require many CC’s. Generating additional nogoods in MSP does not require many CC’s. A2A2 A5A5 A8A8 x23x23 x84x84 x83x83 x54x54 AC NoGood(x 2 3 = Rome,Mon,14:00, x 5 4 =Paris,Mon,14:00>) Conflict

Additional nogoods in MSP Generating additional nogoods in MSP does not require many CC’s. Generating additional nogoods in MSP does not require many CC’s. A2A2 A5A5 A8A8 x23x23 x84x84 x83x83 x54x54 AC NoGood( x 2 3 = Rome,Mon,14:00, x 5 4 =Paris,Mon,14:00>) Conflict NoGood( x 2 3 = Rome,Mon,14:00, x 5 4 =Paris,Mon,15:00>)

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

Experimental Result Messages and CCC’s Vs. number of additional nogood in a message

Privacy Measurements Performance measurements Vs. information sent ratio

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