Given a tree-graph with one of the vertices designated as the root, what is the complexity of calculating the number of vertex-pairs $(u,v)$ of which $v$ is not nearer to the root than $u$ and $u$ is not a vertex of the path from the root to $v$? It is of course possible to determine that number ...

Suppose we have intervals of alternating color on $\mathbb{R}$ (say, red / blue / red / blue / …). All intervals have independent length, with all red intervals distributed as $\mathbb{P}_{R}$, all blue intervals distributed as $\mathbb{P}_B$. Once the intervals are generated, I update them iter...