A Simple Combinatorial Algorithm for Robust Matroid Center

11/07/2022

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by   Georg Anegg, et al.

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Recent progress on robust clustering led to constant-factor approximations for Robust Matroid Center. After a first combinatorial 7-approximation that is based on a matroid intersection approach, two tight LP-based 3-approximations were discovered, both relying on the Ellipsoid Method. In this paper, we show how a carefully designed, yet very simple, greedy selection algorithm gives a 5-approximation. An important ingredient of our approach is a well-chosen use of Rado matroids. This enables us to capture with a single matroid a relaxed version of the original matroid, which, as we show, is amenable to straightforward greedy selections.