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The $k$-center clustering is one of the well-studied clustering problems in computer science. We are given a set of data points $P\subseteq R^d$, where $R^d$ is $d$ dimensional Euclidean space. We need to select $k≤ |P|$ points as centers and partition the set $P$ into $k$ clusters with each point connecting to its nearest center. The goal is to minimize the maximum radius. We consider the so-called online $k$-center clustering model where the data points in $R^d$ arrive over time. We present the bi-criteria $(\frac{n}{k}, (\log\frac{U^*}{L^*})^2)$-competitive algorithm and $(\frac{n}{k}, \logγ\log\frac{nγ}{k})$-competitive algorithm for semi-online and fully-online $k$-center clustering respectively, where $U^*$ is the maximum cluster radius of optimal solution, $L^*$ is the minimum distance of two distinct points of $P$, $γ$ is the ratio of the maximum distance of two distinct points and the minimum distance of two distinct points of $P$ and $n$ is the number of points that will arrive in total.

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