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Entropy-Bounded Representation of Point Grids

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Arash Farzan, Travis Gagie, and Gonzalo Navarro

We give the first *fully compressed* representation of a set of *m*
points on a *n x n* grid, taking *H+o(H)* bits of space, where
*H = log_2 binomial(n^2,m)* is the worst-case 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 entropy-bounded space opens a
new line of research on an otherwise well-studied area, and
is becoming extremely important for handling large datasets.