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This paper explores the use of additional information in distributed constraint satisfaction problem (DisCSP) search, specifically focusing on privacy and efficiency in meeting scheduling. The study includes an experimental evaluation to assess the effectiveness of the proposed approach.
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Using additional information in DisCSP search Amnon Meisels and Oz Lavee Ben Gurion University Israel DCR-04 - Volunteering Information
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
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
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
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
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
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
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
= 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
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
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
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
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
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
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
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
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
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
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
Volunteering additional Nogoods Messages and CCC’s Vs. number of additional Nogoods Density 0.6-0.7 DCR-04 - Volunteering Information
[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
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
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
Volunteering information in General DisCSPs Messages and CCC’s Vs. tightness Density = 0.5 Volunteering all Nogoods DCR-04 - Volunteering Information
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
Thank You DCR-04 - Volunteering Information