Using additional information in DisCSP search

1. Using additional information in DisCSP search Amnon Meisels and Oz Lavee Ben Gurion University Israel DCR-04 - Volunteering Information

2. Overview • Privacy in DisCSP search • The Meeting Scheduling Problem • ABT-CBJ, a multi variable ABT • Privacy in ABT on MSP • Volunteering information in ABT • Experimental evaluation • improving efficiency for MSP • does it work for general DisCSPs ? DCR-04 - Volunteering Information

3. Privacy in DisCSP search • One of the reasons for using distributed search is privacy. Different approaches: • 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. DCR-04 - Volunteering Information

4. Efficiency/Privacy trade-off • Following Wallace et. al. • Use a specific realistic problem – Scheduling Meetings of Agents (MSP) • Knowledge of forbidden time-slots of other agents speeds-up finding of a compatible time-slot • Investigate the trade-off in a wider context • Make it a Distributed Search Problem • Solve by an asynchronous algorithm DCR-04 - Volunteering Information

5. A simple Meeting Scheduling Problem • Agents own calendars with private meetings • Each meeting consist of <Time, Place> Goal: - Schedule a meeting that all Agents can attend with respect to traveling time to and from their own private meetings DCR-04 - Volunteering Information

6. Make it real… • One meeting to be scheduled, can be solved in polynomial time • Synchronous search process, inefficient for solving a distributed search problem • Necessary changes  realistic search problem : • Schedule multiple meetings • A different group of participants in each meeting DCR-04 - Volunteering Information

7. Meeting Scheduling Problem - MSP • 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 every meeting, enabling all the participants to travel among their meetings Comment – no need for private calendars DCR-04 - Volunteering Information

8. Meeting Scheduling as CSP A1 attends m1 ,m3 ,m4 A2 attends m2 ,m4 A3 attends m1 ,m2 A4 attends m2 ,m3 AC- Arrival Constraint m1 m2 AC AC AC AC AC m3 m4 AC DCR-04 - Volunteering Information

9. = Meeting Scheduling as DisCSP A1 A2 x11 x13 = x23 AC x22 AC AC AC x14 = = = = A3 A4 x44 x31 AC AC x42 x32 DCR-04 - Volunteering Information

10. Asynchronous Backtracking with Multiple Variables • Use ABT with some enhancements • Variables of a single agent are ordered consecutively • For backtracking among different agents use resolved Nogoods • For backtracking within a single agent use CBJ • Variables of a single agent are assigned according to the CBJ algorithm – Arrival time constraints are internal DCR-04 - Volunteering Information

11. Measuring Privacy • What kind of information is transferred in asynchronous backtracking ? • What can be kept private? • Privacy of assignments is useless in MSP - equality constraints among participating agents • Arrival constraints can reveal other meetings (or their location) DCR-04 - Volunteering Information

12. OK? Messages • Values are assigned asynchronously • The validity of the information retrieved from an OK? message (about the sending agent’s assignments) is temporary <Ok?, Xi= 12> Xi <Ok?, Xi= 2> <Ok?, Xi= 5> DCR-04 - Volunteering Information

13. Nogood messages • Nogoods contain information about conflicting meetings/locations of multiple agents However: • Not clear how to interpret the information carried by a Nogood • Nogoods can be generated in a sequence of resolutions • Do not imply a conflict with arrival constraint of the sending agent • Nogoods are always valid DCR-04 - Volunteering Information

14. Using Nogoods • Eliminating Nogoods affects the completeness of ABT • Can additional Nogoods improve the efficiency of ABT ? • Generating additionalNogoods in MSP does not require many CCs DCR-04 - Volunteering Information

15. A2 A5 x23 x54 <x23= Rome, Mon, 14:00> <x54= Paris, Mon, 14:00> x83 AC x84 A8 Additional Nogoods in MSP DCR-04 - Volunteering Information

16. A2 A5 x23 x54 <x23= Rome,Mon,14:00> <x54= Paris,Mon,14:00> Conflict x83 AC x84 A8 Additional Nogoods in MSP DCR-04 - Volunteering Information

17. A2 A5 x23 x54 NoGood(x23= Rome,Mon,14:00 ,x54=Paris,Mon,14:00>) Conflict x83 AC x84 A8 Additional Nogoods in MSP DCR-04 - Volunteering Information

18. 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 Additional Nogoods in MSP DCR-04 - Volunteering Information

19. Experimental Evaluation • 16 agents • 9 meetings • 3 meeting per agent (selected randomly) • 24 time-slots in the domains • 2 different distance matrices among locations DCR-04 - Volunteering Information

20. Volunteering additional Nogoods Messages and CCC’s Vs. number of additional Nogoods Density 0.6-0.7 DCR-04 - Volunteering Information

21. [Di+1×…×Dn] [D1×…×Dn] Information value of Nogood • The amount of information carried by a Nogood can be calculated as the ratio of the eliminated subtree to the total search space. • Value(ng<x1=v1,…,xi=vi>)= DCR-04 - Volunteering Information

22. Efficiency vs. Information Messages and CCC’s Vs. fraction of information sent Total fraction is the sum of all fractions sent DCR-04 - Volunteering Information

23. Volunteering information in Random DisCSP • The cost of adding Nogoods to a generalDisCSP is higher • To find additional bad values, all values of the agent have to be scanned and checked against the sending agent - real CCs performed • Random DisCSPs have a large range of density and tightness → range of difficulty • Volunteering Nogoods has not been tried • Can be compared to standard ABT DCR-04 - Volunteering Information

24. Volunteering information in General DisCSPs Messages and CCC’s Vs. tightness Density = 0.5 Volunteering all Nogoods DCR-04 - Volunteering Information

25. Conclusion • Modeling the Meeting Scheduling Problem as a DisCSP • Privacy and information in asynchronous backtracking • Generating additional Nogoods improves the efficiency of asynchronous backtracking DCR-04 - Volunteering Information

26. Thank You DCR-04 - Volunteering Information