On the correct and complete enumeration of the core search space

Reordering more than traditional joins (e.g. outerjoins, antijoins) requires some care, since not all reorderings are valid. To prevent invalid plans, two approaches have been described in the literature. We show that both approaches still produce invalid plans. We present three conflict detectors. All of them are (1) correct, i.e., prevent invalid plans, (2) easier to understand and implement than the previous (buggy) approaches, (3) more flexible in the sense that the restriction that all predicates must reject nulls is no longer required, and (4) extensible in the sense that it is easy to add new operators. Further, the last of our three approaches is complete, i.e., it allows for the generation of all valid plans within the core search space.