All Questions

Let $\Pi$ denote the space of all permutations of $\{1,\dots,n\}$, and let $d(\cdot,\cdot)$ be a metric on $\Pi$. Suppose I am given a large integer $K$ and I have to select $K$ permutations $\pi_1,\...

Suppose I have $n$ points $x_1,\dots,x_n$ that are all independent uniform samples in the unit square, and I'd like to find a short path (in terms of Euclidean length) that touches all of them (a ...

I have a N-point metric space defined by the pairwise distance matrix. I want to encode these N points with binary strings, i.e. each point will be mapped to a vertex in a hypercube. The lengths of ...

Consider a strictly decreasing sequence $d = (d_k)_{k\ge 1}$ of distances in $(0,1)$. Given a constant $C>2$, we say that $d$ has the $C$-grouping property if any finite non-empty subset $S$ (of ...