Author

Lukas Vogl

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Preprint Oct 2026

A Better-than-$2$ Approximation for $k$-Median Part II: Stable Instances

We consider the $k$-median problem on general metric spaces, subject to the condition that the instances are $\beta$-stable (i.e., the optimal solution using $k-1$ centers has a cost at least $(1+\beta)$ times that of the optimal solution with $k$ centers). We give a $(1.89+\epsilon)$-approximation algorithm for such i...

Rares-Darius Buhai, Vincent Cohen-Addad, Henry L. Fleischmann et al. · 1 citation

Preprint Oct 2026

A Better-than-2 Approximation for k-Median Part I: The Power of General Bids

The Greedy algorithm of Jain, Mahdian, Markakis, Saberi, and Vazirani was the best Lagrangian-multiplier-preserving (LMP) approximation algorithm for facility location, and thus the engine behind the best $k$-median guarantees, for over two decades. Its $2$-LMP guarantee was only recently broken by a small amount ($(2-...

Rares-Darius Buhai, Vincent Cohen-Addad, Henry L. Fleischmann et al. · 0 citations