Desk-Mates (Stable Matching) with Privacy of Preferences, and a New Distributed CSP Framework
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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 larger 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(2m3-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.