Problem
Research questions and friction points this paper is trying to address.
prophet inequalities
partition matroids
competitive ratio
lower bound
A Nearly Tight Lower Bound for Matroid Intersection Prophet Inequalities
🤖 AI Summary
研究了q个划分拟阵交集下的先知不等式问题，通过构建和分析给出Ω(q/log q)的下界，解决了该领域的一个开放问题。
📝 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).
Innovation
Methods, ideas, or system contributions that make the work stand out.
prophet inequalities
partition matroids
competitive ratio
single-minded auctions
big-decisions-first
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