Desk-Mates (Stable Matching) with Privacy of Preferences, and a New Distributed CSP Framework

The desk-mates matcher application places students in pairs of two for working in projects (similar to the well known problems of stable matchings or stable roommates). Each of the students has a (hopefully stable) secret preference between every two colleagues. The participants want to find an allocation satisfying their secret preferences and without leaking any of these secret preferences, except for what a participant can infer from the identity of the partner that was recommended to her. The peculiarities of the above problem require solvers based on old distributed CSP frameworks to use models whose search spaces are higher than those in centralized solvers, with bad effects on efficiency. Therefore we introduce a new distributed constraint satisfaction (DisCSP) framework where the actual constraints are secrets that are not known by any agent. They are defined by a set of functions on some secret inputs from all agents. The solution is also kept secret and each agent learns just the result of applying an agreed function on the solution. The expressiveness of the new framework is shown to improve the efficiency (O(2 3−log(m)) times) in modeling and solving the aforementioned problem with m participants. We show how to extend our previous techniques to solve securely problems modeled with the new formalism, and exemplify with the problem in the title. An experimental implementation in the form of an applet-based solver is available.

[1]  M. Silaghi.  Incentive auctions and stable marriages problems solved with floor (n/2) -privacy of human preferences , 2004 .

[2]  Andrew Chi-Chih Yao,et al.  Protocols for secure computations , 1982, FOCS 1982.

[3]  Marius-Calin Silaghi,et al.  The effect of policies for selecting the solution of a DisCSP on privacy loss , 2004, Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems, 2004. AAMAS 2004..

[4]  Eugene C. Freuder,et al.  Privacy/Efficiency Tradeoffs in Distributed Meeting Scheduling by Constraint- Based Agents 1 , 2001 .

[5]  Marius-Calin Silaghi.  Arithmetic circuit for the first solution of distributed CSPs with cryptographic multi-party computations , 2003, IEEE/WIC International Conference on Intelligent Agent Technology, 2003. IAT 2003..

[6]  Makoto Yokoo,et al.  Secure Distributed Constraint Satisfaction: Reaching Agreement without Revealing Private Information , 2002, CP.

[7]  Ehud Gudes,et al.  Algorithms for Solving Distributed Constraint Satisfaction Problems (DCSPs) , 1996, AIPS.

[8]  Bart Preneel,et al.  1 ON SECURELY SCHEDULING A MEETING , .

[9]  Gérard Verfaillie,et al.  An Incomplete Method for Solving Distributed Valued Constraint Satisfaction Problems , 1997, AAAI Workshop: Constraints & Agents.

[10]  Michel Lemaître,et al.  An Incomplete Method for Solving Distributed Valued Constraint Satisfaction Problems , 1997 .

[11]  Bhaskar Krishnamachari,et al.  Communication and Computation in DisCSP Algorithms , 2002 .

[12]  Yves Deville,et al.  Analysis of Distributed Arc-Consistency Algorithms , 1997 .

[13]  Y. Hamadi.  Traitement des problèmes de satisfaction de contraintes distribués , 1999 .

[14]  Bart De Decker,et al.  On Securely Scheduling a Meeting , 2001, SEC.

[15]  Makoto Yokoo,et al.  Adopt: asynchronous distributed constraint optimization with quality guarantees , 2005, Artif. Intell..

[16]  Marius-Calin Silaghi,et al.  Asynchronous Search with Aggregations , 2000, AAAI/IAAI.

[17]  Marius-Calin Silaghi.  Asynchronously solving distributed problems with privacy requirements , 2002 .

[18]  Patrick Prosser,et al.  An Empirical Study of the Stable Marriage Problem with Ties and Incomplete Lists , 2002, ECAI.

[19]  Pedro Meseguer,et al.  Distributed Forward Checking , 2003, CP.

[20]  Oded Goldreich.  Foundations of Cryptography: Volume 1 , 2006 .

[21]  David Manlove,et al.  The Stable Roommates Problem with Ties , 2002, J. Algorithms.

[22]  Avi Wigderson,et al.  Completeness theorems for non-cryptographic fault-tolerant distributed computation , 1988, STOC '88.

[23]  Eugene C. Freuder,et al.  Constraint - based multi - agent meeting scheduling: Effects of agent heterogeneity on performance a , 2002 .

[24]  Shmuel Katz,et al.  On the Feasibility of Distributed Constraint Satisfaction , 1991, IJCAI.

[25]  M. Silaghi.  Solving a distributed CSP with cryptographic multi-party computations , without revealing constraints and without involving trusted servers ∗ , .

[26]  Christian Bessiere,et al.  Distributed Dynamic Backtracking , 2001, CP.

[27]  Richard J. Wallace,et al.  Using Privacy Loss to Guide Decisions During Distributed CSP Search , 2004, FLAIRS Conference.

[28]  Ying Zhang,et al.  Parallel and distributed algorithms for finite constraint satisfaction problems , 1991, Proceedings of the Third IEEE Symposium on Parallel and Distributed Processing.

[29]  Eric Monfroy,et al.  Chaotic iteration for distributed constraint propagation , 1999, SAC '99.

[30]  Joe Kilian,et al.  Founding crytpography on oblivious transfer , 1988, STOC '88.

[31]  Weixiong Zhang,et al.  Distributed Stochastic Search for Constraint Satisfaction and Optimization: Parallelism, Phase Transitions and Performance , 2002 .

[32]  Boi Faltings,et al.  Open Constraint Satisfaction , 2002, CP.

[33]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[34]  Makoto Yokoo,et al.  The Distributed Constraint Satisfaction Problem: Formalization and Algorithms , 1998, IEEE Trans. Knowl. Data Eng..