Intersection joins over interval data are relevant in spatial and temporal
data settings. A set of intervals join if their intersection is non-empty. In
case of point intervals, the intersection join becomes the standard equality
join.
We establish the complexity of Boolean conjunctive queries with intersection
joins by a many-one equivalence to disjunctions of Boolean conjunctive queries
with equality joins. The complexity of any query with intersection joins is
that of the hardest query with equality joins in the disjunction exhibited by
our equivalence. This is captured by a new width measure called the IJ-width.
We also introduce a new syntactic notion of acyclicity called iota-acyclicity
to characterise the class of Boolean queries with intersection joins that admit
linear time computation modulo a poly-logarithmic factor in the data size.
Iota-acyclicity is for intersection joins what alpha-acyclicity is for equality
joins. It strictly sits between gamma-acyclicity and Berge-acyclicity. The
intersection join queries that are not iota-acyclic are at least as hard as the
Boolean triangle query with equality joins, which is widely considered not
computable in linear time