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Constraint Acquisition (CA) systems can be used to assist in the modeling of constraint satisfaction problems. In (inter)active CA, the system is given a set of candidate constraints and posts queries to the user with the goal of finding the right constraints among the candidates. Current interactive CA algorithms suffer from at least two major bottlenecks. First, in order to converge, they require a large number of queries to be asked to the user. Second, they cannot handle large sets of candidate constraints, since these lead to large waiting times for the user. For this reason, the user must have fairly precise knowledge about what constraints the system should consider. In this paper, we alleviate these bottlenecks by presenting two novel methods that improve the efficiency of CA. First, we introduce a bottom-up approach named GrowAcq that reduces the maximum waiting time for the user and allows the system to handle much larger sets of candidate constraints. It also reduces the total number of queries for problems in which the target constraint network is not sparse. Second, we propose a probability-based method to guide query generation and show that it can significantly reduce the number of queries required to converge. We also propose a new technique that allows the use of openly accessible CP solvers in query generation, removing the dependency of existing methods on less well-maintained custom solvers that are not publicly available. Experimental results show that our proposed methods outperform state-of-the-art CA methods, reducing the number of queries by up to 60%. Our methods work well even in cases where the set of candidate constraints is 50 times larger than the ones commonly used in the literature. |
