Singularities make spatial join scheduling hard

The efficiency of database join operations depends crucially on how page fetches are scheduled. In general, finding an optimum schedule is NP-hard. We show that for a class of popular spatial clustering techniques used for spatial data structures, an optimum page fetch schedule that holds two pages in main memory can be computed in time linear in the length of the schedule. In full generality, we prove spatial join scheduling to be NP-hard.