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arXiv · 2011.09406

Non-Adaptive Matroid Prophet Inequalities

Shuchi Chawla·Kira Goldner·Anna R. Karlin·J. Benjamin Miller
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Abstract

We investigate non-adaptive algorithms for matroid prophet inequalities. Matroid prophet inequalities have been considered resolved since 2012 when [KW12] introduced thresholds that guarantee a tight 2-approximation to the prophet; however, this algorithm is adaptive. Other approaches of [CHMS10] and [FSZ16] have used non-adaptive thresholds with a feasibility restriction; however, this translates to adaptively changing an item's threshold to infinity when it cannot be taken with respect to the additional feasibility constraint, hence the algorithm is not truly non-adaptive. A major application of prophet inequalities is in auction design, where non-adaptive prices possess a significant advantage: they convert to order-oblivious posted pricings, and are essential for translating a prophet inequality into a truthful mechanism for multi-dimensional buyers. The existing matroid prophet inequalities do not suffice for this application. We present the first non-adaptive constant-factor prophet inequality for graphic matroids.

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Shuchi Chawla, Kira Goldner, Anna R. Karlin, J. Benjamin Miller. 2020-11-18. Non-Adaptive Matroid Prophet Inequalities. https://arxiv.org/abs/2011.09406

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