arXiv subjects

Alice Sayutina

Publications and source records attributed to Alice Sayutina.

2 recordsLinked to original sources

arXiv2023

Single Sample Prophet Inequality for Uniform Matroids of Rank 2

We study the prophet inequality when the gambler has an access only to a single sample from each distribution. Rubinstein, Wang and Weinberg showed that an optimal guarantee of 1/2 can be achieved when the underlying matroid has rank 1, i.e. in the case of a single choice. We show that this guarantee can be achieved also in the case of a uniform matroid of rank 2 by a deterministic mechanism, and we show that this is best possible among deterministic mechanisms. We also conjecture that a straightforward generalization of our policy achieves the guarantee of 1/2 for all uniform matroids.

cs.GT↗

arXiv2023

Non-Adaptive Prophet Inequalities for Minor-Closed Classes of Matroids

We consider the matroid prophet inequality problem. This problem has been extensively studied in the case of adaptive mechanisms. In particular, there is a tight $2$-competitive mechanism for all matroids. However, it is not known what classes of matroids admit non-adaptive mechanisms with constant guarantee. Recently, it was shown that there are constant-competitive non-adaptive mechanisms for graphic matroids. In this work, we show that various known classes of matroids admit constant-competitive non-adaptive mechanisms.

cs.GT↗