We provide a quasilinear time algorithm for the p-center problem with an additive error less than or equal to 3 times the input graph's hyperbolic constant. Specifically, for the graph G = (V, E) with n vertices, m edges and hyperbolic constant delta, we construct an algorithm for p-centers in time O(p(delta + 1)(n + m) log(n)) with radius not exceeding r(p) + delta when p = 2 and r(p) + 3 delta when p = 3, where r(p) are the optimal radii. Prior work identified p-centers with accuracy r(p) + delta but with time complexity O((n(3) log n + n(2)m) log(diam(G))) which is impractical for large graphs.
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