Entropy-Bounded Representation of Point Grids

We give the first fully compressed representation of a set of m points on an n×n grid, taking H+o(H) bits of space, where H = lg ( n m ) is the entropy of the set. This representation supports range counting, range reporting, and point selection queries, with a performance that is comparable to that of uncompressed structures and that improves upon the only previous compressed structure. Operating within entropybounded space opens a new line of research on an otherwise well-studied area, and is becoming extremely important for handling large datasets.