A new ordered local search algorithm achieves k/2 + o(k) approximation for monotone submodular maximization over k matroids and (ln 4 k)/3 + o(k) for weighted k-set packing.
Tight FPT Approximations for $k$-Median and $k$-Means
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abstract
We investigate the fine-grained complexity of approximating the classical $k$-median / $k$-means clustering problems in general metric spaces. We show how to improve the approximation factors to $(1+2/e+\varepsilon)$ and $(1+8/e+\varepsilon)$ respectively, using algorithms that run in fixed-parameter time. Moreover, we show that we cannot do better in FPT time, modulo recent complexity-theoretic conjectures.
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cs.DS 1years
2026 1verdicts
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Submodular Maximization over Many Matroids via Ordered Local Search
A new ordered local search algorithm achieves k/2 + o(k) approximation for monotone submodular maximization over k matroids and (ln 4 k)/3 + o(k) for weighted k-set packing.