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Non-Adaptive Matroid Prophet Inequalities

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Sayutina_Alice.pdf (567.85 KB)

Date

2023-05-04

Authors

Sayutina, Alice

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University of Waterloo

Abstract

We consider the problem of matroid prophet inequalities. This problem has been ex- tensively studied in case of adaptive prices, with [KW12] obtaining a tight 2-competitive mechanism for all the matroids. However, the case non-adaptive is far from resolved, although there is a known constant- competitive mechanism for uniform and graphical matroids (see [Cha+20]). We improve on constant-competitive mechanism from [Cha+20] for graphical matroids, present a separate mechanism for cographical matroids, and combine those to obtain constant-competitive mechanism for all regular matroids.

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http://hdl.handle.net/10012/19413

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Combinatorics and Optimization