A Nearly Tight Lower Bound for Matroid Intersection Prophet Inequalities

Dimitris Fotakis; Charalampos Platanos; Thanos Tolias

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arXiv · 2609.20696

A Nearly Tight Lower Bound for Matroid Intersection Prophet Inequalities

Dimitris Fotakis·Charalampos Platanos·Thanos Tolias

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Abstract

We study prophet inequalities under intersections of $q$ partition matroids, where an online algorithm irrevocably selects elements with independent nonnegative values drawn from known distributions and revealed in an adversarial order. We prove an $Ω(q/\log q)$ lower bound on the competitive ratio. Together with the known $O(q)$ upper bounds, this resolves, up to a logarithmic factor, the optimal dependence on $q$, an open question posed by Correa, Cristi, Fielbaum, Pollner, and Weinberg (IPCO 2022) and Saxena, Velusamy, and Weinberg (ITCS 2023). Our construction also yields an $Ω(d/\log d)$ lower bound for $d$-single-minded auctions, where buyers request fixed bundles of at most $d$ unit-capacity items. Our construction and analysis build on the "big-decisions-first" framework of Rubinstein and Singla (STOC 2026).

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BibTeX RIS

Dimitris Fotakis, Charalampos Platanos, Thanos Tolias. 2026-09-17. A Nearly Tight Lower Bound for Matroid Intersection Prophet Inequalities. https://arxiv.org/abs/2609.20696

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