Questions tagged [diameter]

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Finding the size $k$ subset in a metric space that maximizes the min distance between elements

I have a metric space $(X,d)$ and I'd like to find a subset of size k of far away elements. We can cast this as the following optimization problem $\max_{S \subseteq X, |S| = k} ( \min_{i \not = j, ...
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Diameter vs. Tractability

I would like to find examples of (unweighted) optimization problems $\Pi$ that satisfy 1) or 2): 1) $\Pi$ is NP-hard but polytime solvable in the class of graphs with diameter $\le k$, for all $k\ge ...
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Diameter of “almost” always connected Erdős-Renyi graphs

Let $G=(V,E)$ be a random Erdős-Renyi Graph, i.e., $G\in\mathcal{G}(n,p)$. It is well known that if $p=(\log n +c +o(1))/n$ with $c\in\Re$ then $$ P(G \text{ is connected})=e^{-e^{-c}}\ . $$ However, ...