The Matroid Secretary Conjecture is True

Sahil Singla

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arXiv · 2609.14555

The Matroid Secretary Conjecture is True

Sahil Singla

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Abstract

We resolve the matroid secretary conjecture, giving an online algorithm that accepts each element of the offline optimum with probability at least $1/4$. The algorithm only needs the number of elements in advance and independence-oracle access to subsets of already-arrived elements; it does not need to know the matroid upfront.

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Sahil Singla. 2026-09-13. The Matroid Secretary Conjecture is True. https://arxiv.org/abs/2609.14555

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