Fast Approximation Algorithms for p-centers in Large $$\delta $$ δ -hyperbolic Graphs

Abstract

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 $$O(p(\delta +1)(n+m)\log _2(n))$$ with radius not exceeding $$r_p + \delta $$ when $$p \le 2$$ and $$r_p + 3\delta $$ when $$p \ge 3$$ , where $$r_p$$ are the optimal radii. Prior work identified p-centers with accuracy $$r_p+\delta $$ but with time complexity $$O((n^3\log _2 n + n^2m)\log _2({{\mathrm{diam}}}(G)))$$ which is impractical for large graphs.