Intersection joins under updates

Abstract

In an intersection join, we are given t sets R1,...,Rt of axis-parallel rectangles in Rd, where d≥1 and t≥2 are constants, and a join topology which is a connected undirected graph G on vertices 1,...,t. The result consists of tuples (r1,...,rt)∈R1×...×Rt where ri∩rj≠∅ for all i,j connected in G. A structure is feasible if it stores O˜(n) words, supports an update in O˜(1) amortized time, and can enumerate the join result with an O˜(1) delay, where n=∑i|Ri| and O˜(.) hides a polylog n factor. We provide a dichotomy as to when feasible structures exist: they do when t=2 or d=1; subject to the OMv-conjecture, they do not exist when t≥3 and d≥2, regardless of the join topology.