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We provide a quasilinear time algorithm for the $p$-center problem with anadditive error less than or equal to 3 times the input graph's hyperbolicconstant. Specifically, for the graph $G=(V,E)$ with $n$ vertices, $m$ edgesand hyperbolic constant $\delta$, we construct an algorithm for $p$-centers intime $O(p(\delta+1)(n+m)\log(n))$ with radius not exceeding $r_p + \delta$ when$p \leq 2$ and $r_p + 3\delta$ when $p \geq 3$, where $r_p$ are the optimalradii. Prior work identified $p$-centers with accuracy $r_p+\delta$ but withtime complexity $O((n^3\log n + n^2m)\log(diam(G)))$ which is impractical forlarge graphs.

Fast approximation algorithms for $p$-centres in large $\delta$-hyperbolic graphs