Fast approximation algorithms for $p$-centres in large $\delta$-hyperbolic graphs
نویسندگان
چکیده
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 δ, we construct an algorithm for p-centers in time O(p(δ + 1)(n + m) log(n)) with radius not exceeding rp + δ when p ≤ 2 and rp + 3δ when p ≥ 3, where rp are the optimal radii. Prior work identified p-centers with accuracy rp + δ but with time complexity O((n3 log n+ n2m) log(diam(G))) which is impractical for large graphs.
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