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Privacy in Distributed Constraint Satisfaction: The Meeting Scheduling Problem Through ABT-CBJ Algorithm

Explore the relationship between information revealing and search efficiency in Distributed Constraint Satisfaction through the ABT-CBJ algorithm. Investigate privacy in asynchronous search and volunteering information. Use multi-variable ABT for the Meeting Scheduling Problem.

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Privacy in Distributed Constraint Satisfaction: The Meeting Scheduling Problem Through ABT-CBJ Algorithm

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  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

  6. Meeting Scheduling Problem Wallace et. al. • Each agent has his own calendar with private meetings • Each meeting consist of <Time,Place> 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.

  7. 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.

  8. Meeting Scheduling problem • Group S of m agents • Group Tof 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.

  9. 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

  10. = Meeting Scheduling as DisCSP A1 A2 x11 x13 = x23 AC x22 AC AC AC x14 = = = = A3 A4 x44 x31 AC AC x42 x32

  11. 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, agent’s 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?

  13. 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 <Ok?, Xi= 5> <Ok?, Xi= 12> <Ok?, Xi= 2>

  14. 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(ng<x1=v1,…,xi=vi>) = Di+1*…*Dn /D1*…*Dn

  15. 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?

  16. Additional nogoods in MSP • Generating additional nogoods in MSP does not require many CC’s. A2 A5 x23 x54 <x23= Rome,Mon,14:00> <x54= Paris,Mon,14:00> x83 AC x84 A8

  17. Additional nogoods in MSP • Generating additional nogoods in MSP does not require many CC’s. A2 A5 x23 x54 <x23= Rome,Mon,14:00> <x54= Paris,Mon,14:00> Conflict x83 AC x84 A8

  18. Additional nogoods in MSP • Generating additional nogoods in MSP does not require many CC’s. A2 A5 x23 x54 NoGood(x23= Rome,Mon,14:00 ,x54=Paris,Mon,14:00>) Conflict x83 AC x84 A8

  19. Additional nogoods in MSP • Generating additional nogoods in MSP does not require many CC’s. A2 A5 x23 x54 NoGood(x23= Rome,Mon,14:00 , x54=Paris,Mon,14:00>) NoGood(x23= Rome,Mon,14:00 , x54=Paris,Mon,15:00>) Conflict x83 AC x84 A8

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

  21. Experimental Result Messages and CCC’s 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

  24. The End

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