All Questions

I have an orthogonal polygon (all edges are horizontal or vertical) which is convex (no holes in any row of column of the polygon). I would like to cover as much as possible of this orthogonal polygon ...

Let $X_1, \dots, X_N$ be $N$ balls of radius $R<<1$ in $[0,1]^d$ such that $N R^d \leqslant R^{\alpha}$ for some $\alpha > 0$ and $d(x_i,x_j)\geqslant 2R$ for any $i\not=j$. The assumption ...