Computational Complexity of Multi-way, Dataflow Constraint Problems

Although it is acknowledged that multi-way dataflow constraints are useful in interactive applications, concerns about their tractability have hindered their acceptance. Certain local propagation algorithms that solve these constraints are polynomial, others (such as SkyBlue) are exponential. Every system handles a specific problem and the influence of any particular restriction on the computational complexity is not yet precisely determined. In this paper, we present three theoretical results that allow us to classify existing multi-way constraint problems. Especially, we prove that the problem handled by SkyBlue is NP-hard.