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In this paper, we propose and investigate the individually fair $k$-centerwith outliers (IF$k$CO). In the IF$k$CO, we are given an $n$-sized vertex setin a metric space, as well as integers $k$ and $q$. At most $k$ vertices can beselected as the centers and at most $q$ vertices can be selected as theoutliers. The centers are selected to serve all the not-an-outlier (i.e.,served) vertices. The so-called individual fairness constraint restricts thatevery served vertex must have a selected center not too far way. Moreprecisely, it is supposed that there exists at least one center among its$\lceil (n-q) / k \rceil$ closest neighbors for every served vertex. Becauseevery center serves $(n-q) / k$ vertices on the average. The objective is toselect centers and outliers, assign every served vertex to some center, so asto minimize the maximum fairness ratio over all served vertices, where thefairness ratio of a vertex is defined as the ratio between its distance withthe assigned center and its distance with a $\lceil (n - q )/k \rceil_{\rm th}$closest neighbor. As our main contribution, a 4-approximation algorithm ispresented, based on which we develop an improved algorithm from a practicalperspective.

Approximate the individually fair k-center with outliers