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arXiv · 2211.03601

A Simple Combinatorial Algorithm for Robust Matroid Center

Georg Anegg·Laura Vargas Koch·Rico Zenklusen
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Abstract

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.

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Georg Anegg, Laura Vargas Koch, Rico Zenklusen. 2022-11-07. A Simple Combinatorial Algorithm for Robust Matroid Center. https://arxiv.org/abs/2211.03601

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