A Lower Bound on the Complexity of Orthogonal Range Queries

The determinantal complexity of a polynomial $P\in \mathbb{F}[x_1,\dots ,x_n]$ over a field $\mathbb{F}$ is the dimension of the smallest matrix M whose entries are affine functions in $\mathbb{F}[x_1,\dots ,x_n]$ such that $P=\mathrm{Det}(M)$. We prove that the determinantal complexity of the polynomial ${\sum }_{i=...\mathrm{}}^{}{}_{}^{}$$\mathrm{}\mathrm{}$$$$$$\mathrm{}$

Orthogonal range reporting is the problem of storing a set of n points in d-dimensional space, such that the k points in an axis-orthogonal query box can be reported efficiently. While the 2-d version of the problem was completely characterized in the ...

In this paper, we survey a few recent applications of Kolmogorov complexity to lower bounds in several models of computation. We consider KI complexity of Boolean functions, which gives the complexity of finding a bit where inputs differ, for pairs of ...