A Cost-Based Model and Algorithms for Interleaving Solving and Elicitation of CSPs ⋆ Nic Wilson, Diarmuid Grimes and Eugene C. Freuder Cork Constraint Computation Centre Department of Computer Science University College Cork, Ireland n.wilson@4c.ucc.ie, d.grimes@4c.ucc.ie, e.freuder@4c.ucc.ie Abstract. We consider Constraint Satisfaction Problems in which con- straints can be initially incomplete, where it is unknown whether certain tuples satisfy the constraint or not. We assume that we can determine such an unknown tuple, i.e., find out whether this tuple is in the con- straint or not, but doing so incurs a known cost, which may vary between tuples. We also assume that we know the probability of an unknown tu- ple satisfying a constraint. We define algorithms for this problem, based on backtracking search. Specifically, we consider a simple iterative al- gorithm based on a cost limit on which unknowns may be determined, and a more complex algorithm that delays determining an unknown in order to estimate better whether doing so is worthwhile. We show exper- imentally that the more sophisticated algorithms can greatly reduce the average cost. 1 Introduction In Constraint Satisfaction Problems it is usually assumed that the CSP is avail- able before the solving process begins, that is, the elicitation of the problem is completed before we attempt to solve the problem. As discussed in the work on Open Constraints and Interactive CSPs [1–5], there are situations where it can be advantageous and natural to interleave the elicitation and the solving. We may not need all the complete constraints to be available in order for us to find a solution. Furthermore, it may be expensive, in terms of time or other costs, to elicit some constraints or parts of the constraints, for example, in a distributed setting. Performing a constraint check in certain situations can be computation- ally very expensive. We may need to pay for an option to be available,or for the possibility that it may be available. Some constraints may be related to choices of other agents, which they may be reluctant to divulge because of privacy is- sues or convenience, and so it could cost us something to find these out. Or they may involve an uncertain parameter, such as the capacity of a resource, and it could be expensive, computationally or otherwise, to determine more certain information about this. ⋆ This material is based upon works supported by the Science Foundation Ireland under Grant No. 05/IN/I886.