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Using additional information in DisCSPs search

Using additional information in DisCSPs search. Prof. Amnon Meisels and Mr. Oz Lavee Ben Gurion University Israel. Over View. Privacy in the DisCSP –earlier work. The meeting scheduling problem. The ABT-CBJ , multi variable ABT algorithm. Privacy in asynchronous search.

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Using additional information in DisCSPs search

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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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