In recent years, several studies proposed privacy-preserving algorithms for solving Distributed Constraint Optimization Problems (DCOPs). Those studies were based on existing DCOP solving algorithms, which they strengthened by implementing cryptographic weaponry that enabled performing the very same computation while protecting sensitive private data. All of those studies assumed that agents do not collude. In this study we propose the first privacy-preserving DCOP algorithm that is immune to coalitions. Our basic algorithm is secure against any coalition under the assumption of an honest majority (namely, the number of colluding agents is <n/2, where n is the overall number of agents). We then proceed to describe two variants of that basic algorithm: a more efficient variant that is secure against coalitions of size ≤c, for some constant c<(n−1)/2; and another variant that is immune to agent coalitions of any size, but relies on an external committee of mediators with an honest majority. Our algorithm – PC-SyncBB – is based on the classical Branch and Bound DCOP algorithm. It offers constraint, topology and decision privacy. We evaluate its performance on different benchmarks, problem sizes, and constraint densities. We show that achieving security against coalitions is feasible. Our experiments indicate that PC-SyncBB can run in reasonable time on problems involving up to 19 agents. As all existing privacy-preserving DCOP algorithms base their security on assuming solitary conduct of the agents, we view this study as an essential first step towards lifting this potentially harmful assumption in all those algorithms.
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