Join Ordering for Constraint Handling Rules

Join ordering is the problem of finding cost optimal execution plans for matching multi-headed rules. In the context of Constraint Handling Rules, this topic has received limited attention so far, even though it is of great importance for efficient CHR execution. We present a formal cost model for joins and investigate the possibility of join optimization at runtime. We propose some heuristic approximations of the parameters of this cost model, for both the static and dynamic case. We discuss an O(n log n) optimization algorithm for the special case of acyclic join graphs. However, in general, join order optimization is an NP-complete problem. Finally, we identify some classes of cyclic join graphs that can be reduced to acyclic ones.