An experimental study on the complexity

Not only in deductive databases, logic programming, and constraint satisfaction problems but also in object bases where each single dot in a path expression corresponds to a join, the optimizer is faced with the problem of ordering large numbers of joins. This might explain the renewed interest in the join ordering problem. Although many join ordering techniques have been invented and benchmarked over the last years, little is known on the actual eeectiveness of the developed methods and the cases where they are bound to fail. The problem attacked is the discovery of parameters and their qualitative innuence on the complexity of single problem instances and on the eeectiveness of join ordering techniques including search procedures , heuristics, and probabilistic algorithms. Thus an extensive analysis of the search space is carried out, with particular emphasis on the existence of phase transitions in this space and on the innuence the parameters have on these transitions. Having these parameters on hand serves two important tasks. (1) For a given heuristic, parameter combinations can be identiied where it performs nearly optimal and others where it performs badly. Hence, on the one hand, we can be conndent about the results of a heuristic for well determined cases and, on the other hand, can avoid the application of a heuristic where it is bound to fail. (2) When benchmarking join ordering heuristics, one had|up to now|to choose a benchmark arbitrarily. Given the parameters which innuence the complexity of a join ordering problem it becomes possible to consciously design challenging benchmarks.