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arXiv · 2610.03660

Single-Sample Prophet Inequalities: A Combinatorial to Single-Item Reduction

Shuchi Chawla·Trung Dang
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Abstract

We study single-sample prophet inequalities for online combinatorial allocation. Our main contribution is a general reduction from combinatorial to single-item prophet inequalities for valuation classes admitting suitable supporting prices. The reduction uses a free-disposal value to separate buyer-side combinatorial constraints from item-side supply constraints, yielding a modular framework that applies in the stronger Game of Googol model. This framework yields a $\frac{1}{6\sqrt{3}}\approx\frac{1}{10.4}$-competitive single-sample prophet inequality and a $(β_{k-1}/4)$-competitive $k$-sample prophet inequality for XOS valuations, where $β_k$ is the competitive ratio of a $k$-sample single-item prophet inequality, improving upon the work of [DKL+24]. Both results extend directly to divisible resources with capped-XOS valuations. Along the way, we obtain new results for online free disposal and an optimal single-sample prophet inequality for fractional knapsack in the Game of Googol model.

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Shuchi Chawla, Trung Dang. 2026-10-02. Single-Sample Prophet Inequalities: A Combinatorial to Single-Item Reduction. https://arxiv.org/abs/2610.03660

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