Distributed Forward Checking May Lie for Privacy

DisFC is an ABT-like algorithm that, instead of sending the value taken by the high priority agent, it sends the domain of the low priority agent that is compatible with that value. With this strategy, plus the use of sequence numbers, some privacy level is achieved. In particular, each agent knows its value in the solution, but ignores the values of the others. However, the idea of sending the whole compatible domain each time an agent changes its value may cause a privacy loss on shared constraints that was initially overlooked. To solve this issue, we propose DisFClies, an algorithm that works like DisFC but it may lie about the compatible domains of other agents. It requires a single extra condition: if an agent sends a lie, it has to tell the truth in finite time afterwards. We prove that the algorithm is sound, complete and terminates. We provide experimental results on the increment in privacy achieved, at the extra cost of more search.