On Parallel k-Center Clustering
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We consider the classic k-center problem in a parallel setting, on the low-local-space Massively Parallel Computation (MPC) model, with local space per machine of 𝒪(n^δ), where δ∈ (0,1) is an arbitrary constant. As a central clustering problem, the k-center problem has been studied extensively. Still, until very recently, all parallel MPC algorithms have been requiring Ω(k) or even Ω(k n^δ) local space per machine. While this setting covers the case of small values of k, for a large number of clusters these algorithms require large local memory, making them poorly scalable. The case of large k, k ≥Ω(n^δ), has been considered recently for the low-local-space MPC model by Bateni et al. (2021), who gave an 𝒪(loglog n)-round MPC algorithm that produces k(1+o(1)) centers whose cost has multiplicative approximation of 𝒪(logloglog n). In this paper we extend the algorithm of Bateni et al. and design a low-local-space MPC algorithm that in 𝒪(loglog n) rounds returns a clustering with k(1+o(1)) clusters that is an 𝒪(log^*n)-approximation for k-center.
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